Assignment on Harmonically Excited Vibration
1. A machine part of mass 1.95 kg vibrates in a viscous medium. Determine the damping coefficient
when a harmonic exciting force of 24.46 N results in a resonant amplitude of 1.27 cm with a
period of 0.20 s.
2. If the system of Prob. 1 is excited by a harmonic force of frequency 4 cps, what will be the
percentage increase in the amplitude of forced vibration when the dashpot is removed?
3. A weight attached to a spring of stiffness 525 N/m has a viscous damping device. When the weight
is displaced and released, the period of vibration is 1.80 s, and the ratio of consecutive amplitudes
is 4.2 to 1.0. Determine the amplitude and phase when a force 𝐹 = 2 cos 3𝑡 acts on the system.
4. Show that for the damped spring-mass system, the peak amplitude occurs at a frequency ratio
𝜔
given by the expression (𝜔 ) = √1 − 2𝜁 2
𝑛
𝑝
5. A spring-mass is excited by a force 𝐹0 𝑠𝑖𝑛𝜔𝑡. At resonance, the amplitude is measured to be 0.58
cm. At 0.80 resonant frequency, the amplitude is measured to be 0.46 cm. Determine the
damping factor 𝜁 of the system.
6. Shown in Fig. 1 is a cylinder of mass m connected to a spring of stiffness k excited through viscous
friction c to a piston with motion 𝑦 = 𝐴𝑠𝑖𝑛𝜔𝑡 Determine the amplitude of the cylinder motion
and its phase with respect to the piston.
7. A counterrotating eccentric mass exciter shown in Fig. 2 is used to determine the vibrational
characteristics of a structure of mass 181.4 kg. At a speed of 900 rpm, a stroboscope shows the
eccentric masses to be at the top at the instant the structure is moving upward through its static
equilibrium position, and the corresponding amplitude is 21.6 mm. If the unbalance of each wheel
of the exciter is 0.0921 kg m, determine (a) the natural frequency of the structure, (b) the
damping factor of the structure, (c) the amplitude at 1200 rpm, and (d) the angular position of
the eccentrics at the instant the structure is moving upward through its equilibrium position.