MCQ MDL 1A FREE UNDAMPED VIBRATIONS Q.1 An automobile having a mass 1500 kg deflects its spring by 5 cms under its dead weight. The natural frequency of the car in vertical direction in Hz will be, a) 2.229 b) 4.29 6 c) 3.784 d) 5.626 Q.2 Spring mass system having spring stiffness 'K' N/m and mass of 'M' kg has its natural frequency of vibration 12 Hz. on adding 2 kg. mass ,frequency reduces by 2 Hz. Then the mass in kg will be, a) 5.64 b) 4.54 c) 6.62 d) 7.34 Q.3 Spring mass system having spring stiffness 'K' N/m and mass of 'M' kg has its natural frequency of vibration 12 Hz. on adding 2 kg. mass ,frequency reduces by 2 Hz. Then the stiffness in N/m will be, a) 25808.9 b) 29876.9 c) 21456.7 d) 22123.8 Q.4 A body performs two vibratory motion simultaneously. X1 = 1.93 sin 9.5 t X2 = 2.00 sin 10.0 t ,units being cm., rad. and sec. The maximum beat amplitude and the beat in m and rad/sec frequency will be a) 0.7 , 19.5 b) 3.93, 19.5 c) 3.93 , 0.5 d) 0.07 , 0.5 Q.5 a) 2 Degree of freedom of a ship sailing will be b) 3 c) 4 d) 6 Q.6 A body suspended from a spring vibrates vertically up and down between two positions 3cms and 5 cms above ground. During each sec. it reaches the top position(5cm above ground) 15 times. Its time period in sec. and amplitude in cm. of above body will be , a) 0.06 , 1 b) 0.08 , 1.5 c) 0.07 , 2 d) 0.07 , 3 Q.7 In all wall clocks which work on the principle of simple pendulum, the length of string in mts. that can be worked out for a time period of 1 sec. will be, a) 0.6495 b) 0.2485 c) 0.4976 d) 0.5219 Q.8 If two vibrations of same frequency are such that when one reaches its maximum displacement (peak acceleration point) the displacement of the other is zero. Phase difference between the two vibration is, a) π/6 b) π/4 c) π/2 d) π/8 Q.9 The direction of inertia force of piston of a vertical engine when piston moves from mid-position to T.D.C. Will be a) Downwards b)Left c) Right d) Upwards Q.10 Four balls of mass 2 kg. , 3 kg. , 5kg. and 6 kg. respectively are suspended using strings of equal lengths. The time period of oscillations will be , a) Same in the all the cases b) Max. in the case of 2 kg. mass c) Max. in the case of 6 kg. mass d) Min. in the case of 2 kg. mass Q.11 A 5 kg. body is suspended from a spring of constant 'K' . K = 1000 N/mm .Mass of the spring is 0.6 kg. Natural frequency of the above system considering the mass of the system in kg will be, a) 3.032 b) 2.207 c) 4.702 d) 8.302 MCQ MDL 1B Q.1 A car having a mass 1270 kg deflects its spring by 4 cms under its dead weight. The natural frequency of the car in Hz in vertical direction will be, 2.492 4.296 3.784 5.626 Q.2 Spring mass system having spring stiffness 'K' N/m and mass of 'M' kg has its natural frequency of vibration 10 Hz. on adding 2 kg. mass ,frequency reduces by 2 Hz. Then the mass in kg will be, 5.64 3.555 6.62 7.34 Q.3 Spring mass system having spring stiffness 'K' N/m and mass of 'M' kg has its natural frequency of vibration 10 Hz. on adding 2 kg. mass ,frequency reduces by 2 Hz. Then the stiffness in N/m will be, 14034.57 29876.9 21456.7 22123.8 Q.4 A body performs two vibratory motion simultaneously. X1 = 1.90 sin 9.1 t X2 = 2.80 sin 11.8 t ,units being cm., rad. and sec. The maximum beat amplitude in meters and the beat frequency in rad/sec will be 2.71 , 19.5 3.93, 19.5 4.70 , 2.70 3.07 , 0.5 Q.5 A torsional vibrating having shaft stiffness 'Kt' N-m/rad and mass moment of inertia of 'I' Kg-m2 has its natural frequency of vibration 15 Hz. On doubling the mass moment of inertia of 'I'2 and reducing the shaft stiffness 'Kt' to it’s half, the new frequency in Hz will be, 5.64 7.50 6.62 7.34 Q.6 A body suspended from a spring vibrates vertically up and down between two positions 2cms and 6 cms above ground. During each sec. it reaches the top position(6cm above ground) 12 times. Its time period in sec. and amplitude in cm. of above body will be , 0.08 , 2 0.08 , 1.5 0.07 , 2 0.07 , 3 Q.7 A torsional vibrating having shaft stiffness 'Kt' N-m/rad and mass moment of inertia of 'I' Kg-m2 has its natural frequency of vibration 12.6 Hz. On doubling the shaft stiffness 'Kt' and reducing the mass moment of inertia of 'I'2 to it’s half, the new frequency in Hz will be, 45.6 25.2 28.4 35.2 Q.8 If two tides of same frequency would reach the sea bank with a time lag of quarter time period (tp) Phase difference between the two will be, π/6 π/4 π/2 π/8 Q.9 The direction of inertia force of piston of a vertical engine when piston moves from mid-position to B.D.C. Will be Downwards Left Right Upwards Q.10 A machine is installed on four springs each of stiffness K = 33 N/m .Mass of the machine is 2.8 kg. Natural frequency of the above system in Hz will be, 2.032 1.09 2.702 3.302 DAMPED FREE VIBRATION Q.1 In a under damped system with a mass of 400 Kg. Amplitude was found to be reducing by values measured on one side of equilibrium are 4.87,1.62,.54,.18 ,.06 etc .respectively. Number of cycles required for the amplitude to reduce to zero is Zero Infinity Four Five Q.2 In large guns the type of damping used will be Over-damping Under-damping Critical damping options None of the Q.3 A horizontal spring mass system with coulomb damping has mass of 5 Kg. attached to spring of stiffness 980 N/m and frictional resistance is 1.225 N. The amplitude lost after 7 cycles will be 0.56 m 0.47 m 0.43 m 0.35 m Q.4 Most of the dampers used in engineering applications use No damping Over damping Critical damping Under damping Q.5 A system has the following data m = 10 Kg., K = 2400 N/m and ζ = 0.249.Mas of the spring is 3 kg Damped frequency of the system considering mass of the spring will be 3.29 Hz. 2.93 Hz 2.26 Hz 3.92 Hz. Q.6 Which type of vibrations are also known as transient vibrations? Undamped vibrations Damped vibrations Torsional vibrations Transverse Vibrations Q.7 The logarithmic decrement if damping factor is 0.33 will be 4.39 2.19 5.29 None of the options Q.8 In a damped vibration system the mass having 20 kg makes 40 oscillations in 20 seconds. The amplitude of vibrations decreases to 1/8 th of its initial value after 8 oscillations. The damped frequency of vibration will be 1.2 Hz 1.4 Hz 1.6 Hz None Q.9 The natural frequency of damped vibration, if damping factor is 0.52 and natural frequency of the system is 30 rad/sec which consists of machine supported on springs and dashpots will be 35.78 rad/sec 25.62 rad/sec 38.82 rad/sec None of the options Q.10 The logarithmic decrement, if the amplitude of a vibrating body reduces to 1/6th in two cycles will be 0.4763 0.8958 0.7839 None of the options Q.11 The logarithmic decrement, if the amplitude of a vibrating body reduces to 1/8 th of it’s intial value in eight cycles will be 0.2599 0.8958 0.7839 None of the options Q.12 A gun barrel of mass 500kg has a recoil spring of stiffness 3,00,000 N/m. If the barrel recoils 1.2 meters on firing, initial velocity of the barrel in m/sec will be 29.39 21.43 32.37 36.73 Q.13 A gun barrel of mass 500kg has a recoil spring of stiffness 3,00,000 N/m. If the barrel recoils 1.2 meters on firing, the critical damping coefficient of the dashpot in N-sec/m will be 24495 19873 31687 41765 Q.14 A disc of a torsional pendulum has a moment of inertia of 600 kg-m2 and is immersed in a viscous fluid. The shaft attached to it is 0.4m long and 0.1m in diameter. When the pendulum is oscillating, the observed amplitudes on the same side of the mean position for successive cycles are 9 degrees, 6 degrees and 4 degrees. The logarithmic decrement will be 0.405 0.895 0.783 None of the options Q.15 The logarithmic decrement if damping factor is 0.03 will be 0.188 0.895 0.783 None of the options Q.16 A damped vibration system uses viscous damping. The amplitude Would reduce by Constant ratio Constant value variable value None of the options Q.17 A damped vibration system has Coulomb’s damping. The amplitude Would reduce by Constant ratio Constant value variable value None of the options Q.18 In most engineering applications the type of damping used will be Over-damping Under-damping the options Critical damping None of Q.19 The natural frequency of damped vibration, if damping factor is 0.52 and natural frequency of the system is 30 rad/sec will be 25.62 rad/sec 20.78 rad/sec 14.4 rad/sec 15.33 rad/sec Q.20 In a under damped system with a mass of 600 Kg. Amplitude was found to be reducing by values measured on one side of equilibrium are 4.87,1.62,.54,.18 ,.06 etc .respectively. Number of cycles required for the amplitude to reduce to zero is Zero Infinity Four Five FORCED VIBRATIONS 1. In forced vibrations the magnitude of damping force at resonance equals Inertia force Impressed force Infinity Spring force In steady state forced vibrations, the amplitude of vibrations at resonance is Directly proportional to the damping coefficient Directly proportional to the resonant frequency Inversely proportional to the damping coefficient Inversely proportional to the resonant frequency The ratio of the maximum displacement of the forced vibration to the zero frequency deflection is called Logarithmic decrement Damping coefficient Critical damping coefficient Magnification factor 2. For steady state forced vibrations, the phase lag at resonance condition in degrees is 0 45 90 180 3. A rotary system having damping coefficient of 50N sec m/rad, when twisted with an angular velocity of 2 rad/sec will experience the damping torque of 50 Nm 100 Nm 25 Nm 200 Nm 4. Which of the following effects is more dangerous for a ship Rolling Waving Pitching Steering 5. The critical speed of a vehicle which moves on a road having sinusoidal profile of wavelength 2.5 m if the mass of the vehicle is 300 kg and natural frequency of its spring suspension system is 8 rad/sec will be 4.15 m/sec 3.18 m/sec 2.36 m/sec None of the above 6. The effect of damping on phase angle at resonance frequency will be Phase angle increases as damping increases Damping has no effect on phase angle Phase angle increases as damping decreases None Of The Options 7. The damped natural frequency, if a spring mass damper system is subjected to periodic disturbing force of 30 N. Damping coefficient is equal to 0.76 times of critical damping coefficient and undamped natural frequency is 5 rad/sec will be 3.99 rad/sec 2.13 rad/sec 4.12 rad/sec 3.24 rad/sec 8. When frequency ratio (ω/ωn) is greater than unity, phase angle decreases as ______ Damping Factor Increases Damping Factor Decreases constant None Of The Options Damping Factor remains 9. Magnification factor is the ratio of ______ Zero frequency deflection and amplitude of steady state vibrations Amplitude of steady state vibrations and zero frequency deflection None of the options 10. The equation m(d2x/ dt2) + c (dx/dt) + Kx = F0 sin ωt is a second order differential equation. The solution of this linear equation is given as Complementary function Particular function Sum of complementary and particular function Difference of complementary and particular function 11. The phase difference or phase angle in forced vibrations means Difference between displacement vector (xp) and velocity vector Vp Angle in which displacement vector leads force vector by (F0 sinωt) Angle in which displacement vector (xp) lags force vector (F0 sinωt) None Of The Options MCQ SET 4 BALANCING ROTATING MASSES Minimum number of balance masses required to achieve static balance of number of masses rotating in the same plane will be Two Four Six One The unbalanced force due to revolving masses Varies in magnitude but constant in direction Varies in direction but constant in magnitude Varies in magnitude and direction both Constant in magnitude and direction both The unbalance in a rotor is produced due Centripetal forces Centrifugal forces Inertia forces Resistive forces Minimum number of balancing planes required to achieve dynamic balance of number of masses rotating in non-coplanar planes will be Two Four Six One In a rotating component the effect of any unbalance located at some radius is to Bend the shaft Compress the shaft Twist the shaft Shear the shaft In order to achieve the complete balance of number of masses rotating in non-coplanar planes The algebraic summation of all the forces must be zero The algebraic summation of all the couples must be zero The algebraic summation of all the forces and couples must be zero None of the options A mass m attached to a shaft rotating at ω rad/sec at radius r cm from axis of the shaft is balanced by mass β at radius b cm from the axis of shaft . If the speed of the shaft is doubled , the value of balance mass β will be Doubled Quadrupled Unaffected Halved A mass of 12 kg is attached to a shaft radius at 80cm. The balance masses B1 and B2 are attached at a radius of 80 cm. The planes of rotation of the three masses are parallel. If the shaft is rotating at 100 rpm and to achieve the dynamic balance, the balance mass B2 should be 9 kg 6 kg 12kg 4 kg The balance masses are introduced in the plane parallel to the plane of rotation of the disturbing mass. To obtain complete dynamic balance, minimum number of balance masses to be introduced will be One Two Three None of the options A mass of 16 kg is attached to a shaft radius 60cm. The balance masses B1 and B2 are attached at a radius of 60 cm. The planes of rotation of the three masses are parallel. If the shaft is rotating at 100 rpm and to achieve the dynamic balance, the balance mass B1 is 9 kg 12 kg 24 kg 18 kg The static balancing is satisfactory for low speed rotors but with increasing speeds, dynamic balancing becomes necessary. This is because, the Unbalanced couples are caused only at higher speeds Unbalanced forces are not dangerous at higher speeds Effects of unbalances are proportional to the square of the speed Effects of unalances are directly proportional to the speed MCQ MDL 5 BALANCING OF REC COMPONENTS Q.1 A single cylinder reciprocating engine has speed 240 rpm, stroke 300 mm, mass of reciprocating parts 50 kg, mass of revolving parts at 150 mm radius 37kg. If two-third of the reciprocating parts and all the revolving parts are to be balanced, then balancing mass required at a radius of 400 mm will be 26.38 kg 27.38 kg 28.38 kg None of the options Q.2 The primary unbalanced force is maximum when the angle of crank with the line of stroke is 45 degrees 90 degrees 135 degrees 180 degrees Q.3 The frequency of fluctuations of secondary inertia forces of reciprocating parts of a multi cylinder engine in one revolution of crank shaft will be Two Four Six One Q.4 Multi-cylinder engines are desirable because Balancing problems are reduced No balancing is required Efficiency is enhanced None of the options Q.5 The secondary unbalanced force is maximum when the angle of crank with the line of stroke is 45 degrees 90 degrees 135 degrees None of the options Q.6 The partial balancing means Balancing partially the revolving masses Balancing partially the reciprocating masses Best balancing of engines None of the options Q.7 Secondary forces in reciprocating mass on engine frame are Of same frequency as of primary forces Twice the frequency as of primary forces Four times the frequency of primary forces None of the options Q. 8 Number of times the primary unbalanced force is maximum in one revolution of the crank Two times Three times Four times Six times Q.9 In case of low speed reciprocating engines ,the following is used Complete balancing Partial balancing Dynamic balancing Static balancing Q.10 In multi cylinder inline engines, the balance weights in order to achieve complete primary balance are placed on auxiliary drives rotating at Same speed as main crank shaft Half the speed of the main crank shaft Twice the speed of the main crank shaft Quadraple times than main Crank shaft MCQ MDL 6 TORSIONAL VIB Q.1 In a torsional vibrating system when the rotor A, the rotor B, the rotor C, rotate in the directions shown in Fig. The number of nodes formed will be Zero nodes One node Two nodes Three nodes Q.2 For a ship “ The critical speed speed range” or “The barred speed speed range “ is evaluated based on The axial vibrations The transverse vibrations The longitudinal vibrations The torsional vibrations Q.3 A torsional vibrating system carrying four rotors and has a degree Of freedom(DOF) of four. It’s four natural frequencies are fn0= 0 Hz, fn1= 27 Hz, fn2= 134 Hz, fn3= 278 Hz. When this system was vibrating, three nodes were observed to be formed. Then in that case the might be vibrating at 0 Hz 27 Hz 134 Hz 278 Hz Q.4 In case of a torsional vibrating system, the internal particles of the system would be found to be moving in Along the lines parallel to the axis of the vibrating system Along the lines Perpendicular to the axis of the vibrating system In concentric circles about the axis of the vibrating system None of the options Q.5 The torsional vibrations are more important to be considered on board because They are not visible like other vibrations and felt to be evident only after the failure of the component They induce more stresses than other vibrations They have higher frequencies than other vibrations They have higher magnitudes than other vibrations Q.6 In the torsional vibrating system when the rotor A, the rotor B, the rotor C, rotate in the same direction shown in Fig. The number of nodes formed will be Zero nodes One node Two nodes Three nodes Q.7 The formula used to calculate mass moment of inertia (I G) of a torsional pendulum or Flywheel about the axis through Centre of gravity? 0.5 m r2 m r2 0.25 m r2 None of the options Q.8 The natural frequency of vibrations of a torsional pendulum with the following dimensions. Length of rod(L) = 1 m, Diameter of rod(d) =5 mm, Diameter of the rotor(D)= 0.2 m Mass of the rotor (M) = 2 Kg. Modulus of rigidity for the material of the rod may be assumed to be 0.83 x 10 11 N/ m2 will be 4.72 Hz. 6.29 Hz 3.59 Hz. 5.54 Hz. Q.9 A six cylinder in-line engine directly drives a propeller through a coupling. The degree of freedom of this torsional system will be 3 8 6 4 Q.10 In a Semi-definite or Degenerate system one of the natural frequencies will be Infinity Hz Two Hz Unity Hz Zero Hz MCQ MDL 6 Q.1 In a torsional vibrating system when the rotor A, the rotor B, the rotor C, rotate in the directions shown in Fig. The number of nodes formed will be Zero nodes One node Two nodes Three nodes Q.2 For a ship “ The critical speed speed range” or “The barred speed speed range “ is due to the following phenomenon Beat phenomenon Resonance phenomenon Interference phenomenon None of the options Q.3 A torsional vibrating system carrying four rotors and has a degree Of freedom(DOF) of four. It’s four natural frequencies are fn0= 0 Hz, fn1= 32 Hz, fn2= 143 Hz, fn3= 287 Hz. When this system was vibrating, two nodes were observed to be formed. Then in that case the might be vibrating at 0 Hz 32 Hz 143 Hz 287 Hz Q.4 In case of a torsional vibrating system, the internal induced stresses Will be Tensile stresses Bending stresses Torsional shear stresses Compressive stresses Q.5 In torsional vibrations at node points Torsional shear stresses are maximum Torsional shear stresses are minimum No torsional shear stresses are induced None of the options Q.6 In the torsional vibrating system when the rotor A, the rotor B, the rotor C, rotate in the direction as shown in Fig. The number of nodes formed will be Zero nodes One node Two nodes Three nodes Q.7 The formula used to calculate polar moment of inertia of shaft carrying torsional pendulum or Flywheel about the axis through centre of gravity? (Pi X d4)/32 (Pi X d4)/64 (Pi X d6)/32 None of the options Q.8 The natural frequency of vibrations of a torsional pendulum with the following dimensions. Length of rod(L) = 1.2 m, Diameter of rod(d) =8 mm, Diameter of the rotor(D)= 0.4 m Mass of the rotor (M) = 2.5 Kg. Modulus of rigidity for the material of the rod may be assumed to be 0.83 x 1011 N/ m2 will be 4.72 Hz. 6.29 Hz 3.75 Hz. 5.54 Hz. Q.9 A four cylinder in-line engine directly drives a propeller through a coupling. The degree of freedom of this torsional system will be 3 8 6 4 Q.10 In torsional vibrations as frequency increases, the number of nodes will Increase Decrease Remain unchanged None of the options MCQ MDL 7 TRANSVERSE VIB Q.1 Vibrations of a shaft due to the weights of various components like Gears, pulleys, sprockets etc will be Longitudinal vibrations Torsional vibrations Transverse vibrations Axial vibrations Q.2 In case of a Transverse vibrating system, the internal particles of the system would be found to be moving in Along the lines parallel to the axis of the vibrating system Along the lines Perpendicular to the axis of the vibrating system In concentric circles about the axis of the vibrating system None of the options Q.3 Natural Frequency of Free Transverse Vibrations For a Shaft Subjected to a Number of Point Loads is determined by Dunkerly’s method Newton’s method D’Alembert’s method None of the options Q.4 In case of a Transverse vibrating system, the internal induced stresses Will be Tensile stresses Bending stresses Torsional shear stresses Compressive stresses Q.5 The static deflection of a Cantilever beam with end load is given by 𝐩 𝐥𝟑 𝟑𝐄𝐈 None of the options 𝐩 𝐥𝟒 𝐩 𝐥𝟐 𝟑𝐄𝐈 𝟔𝐄𝐈 Q.6 The static deflection of a Simply supported beam with a central load is given by 𝐰 𝐥𝟑 𝟒𝟖𝐄𝐈 𝐰 𝐥𝟐 𝐰 𝐥𝟒 𝟐𝟒𝐄𝐈 𝟒𝟖𝐄𝐈 None of the options Q.7 The static deflection of a Simply supported beam with a off-centre load is given by 𝐰 𝒍𝟐𝟏 𝒍𝟐𝟐 𝟑𝐄𝐈𝐥 𝐰 𝒍𝟑𝟏 𝒍𝟐𝟐 𝐰 𝒍𝟐𝟏 𝒍𝟑𝟐 𝟒𝟖𝐄𝐈𝐥 𝟒𝟖𝐄𝐈𝐥 None of the options Q.8 The static deflection of a Cantilever beam with non-end load is given by 𝐰 𝒍𝟑𝟏 𝟑𝐄𝐈 𝐰 𝒍𝟐𝟏 𝐰 𝒍𝟒𝟏 𝟑𝐄𝐈 𝟑𝐄𝐈 None of the options Q.9 The static deflection of a Fixed-fixed beam with a central load is given by 𝐰 𝐥𝟑 𝟏𝟗𝟐𝐄𝐈 𝐩 𝐥𝟐 𝐩 𝐥𝟒 𝟏𝟗𝟐𝐄𝐈 𝟏𝟗𝟐𝐄𝐈 None of the options Q.10 The static deflection of a beam due to uniformly distributed load is given by 𝟓𝐖 𝐥𝟒 𝟑𝟖𝟒𝐄𝐈 𝟓𝐖 𝐥𝟑 𝟓𝐖 𝐥𝟐 𝟑𝟖𝟒𝐄𝐈 𝟑𝟖𝟒𝐄𝐈 None of the options MCQ MDL 8 WHIRLING-SHAFT Q.1 The critical speed or whirling speed of a shaft is due to Centrifugal force Centripetal force Unbalance force None of the options Q.2 The critical speed or whirling speed of a shaft is the speed at which The shaft starts vibrating in a direction Parallel to the axis of the vibrating system Perpendicular to the axis of the vibrating system In concentric circles about the axis of the vibrating system None of the options Q.3 The deflection of the shaft at whirling speed is given by 𝛚 𝟐 ) 𝐞 𝛚𝐧 𝐲= 𝛚 𝟐 𝟏−( ) 𝛚𝐧 ( 𝛚 𝟑 ( ) 𝐞 𝛚𝐧 𝐲= 𝛚 𝟐 𝟏−( ) 𝛚𝐧 𝛚 𝟒 ( ) 𝐞 𝛚𝐧 𝐲= 𝛚 𝟐 𝟏−( ) 𝛚𝐧 None of the options Q.4 The speed of a shaft at which the deflection of the shaft tends to Infinity is known as Whirling speed Peak speed Maximum speed None of the options Q.5 When the shaft speed is less than the critical speed, the deflection ‘y’ will be Positive Nagative Neutral None of the options Q.6 When the shaft speed is equal to the critical speed, the deflection ‘y’ will Increase Decrease Tend to Infinity None of the options Q.7 When the shaft speed is more than the critical speed, the deflection ‘y’ will be Positive Nagative Neutral None of the options Q.8 The critical speed or whirling speed of a shaft is Inversely proportional to eccentricity Directly proportional to eccentricity Independent of eccentricity None of the options Q.9 Centrifugal force that makes the shaft vibrate violently is Inversely proportional to eccentricity Directly proportional to eccentricity Independent of eccentricity None of the options Q.10 The deflection of the shaft at whirling speed is Inversely proportional to frequency ratio Directly proportional to frequency ratio Independent of frequency ratio None of the options