Assignment 1
1.
z  20 sin t . Show the relative positions
and magnitudes of the displacement, velocity and acceleration vectors at time t=0 and  =2.0 rad/s and
The motion of a particle is represented by the equation
0.5 rad/s.
2.
3.
4.
5.
A body performs, simultaneously, the motions
amplitudes was 10/3. Determine the amplitudes and phase angle when a force F  3 sin 4t acts on
the system. The unit of the force is Newton.
Find the natural frequencies and mode shapes of a spring mass system shown in Figure 1. Assume
8.
m1  m2  m .
Show that, in frequency-dependent excitation the damping factor ξ is given by the following
expression:  
7.
z2 (mm)  21 sin 8.5t
Determine the maximum and minimum amplitude of the combined motion and the time period of the
periodic motion.
A vibrating system consists of a mass of 5 kg, a spring stiffness of 5 N/mm and a dashpot with a
damping coefficient of 0.1 N-s/m. Determine (i) damping ratio (ii) logarithmic decrement.
A mass attached to a spring of stiffness of 5 N/mm has a viscous damping device. When the mass was
displaced and released, the period of vibration was found to be 2.0 s and the ratio of the consecutive
k1  k 2  k3  k and
6.
z1 (mm)  20 sin 8.0t
1  f 2  f1 


2  2 fn 
Where f1 and f2 are frequencies at which the amplitude is 1/ 2 times the peak amplitude.
A machine having a mass of 100 kg and supported on springs of total stiffness 7.84×10 5 kN/m has an
unbalanced rotating element which results in a disturbing force of 392 N at a speed of 3000 rpm.
Assuming a damping factor of 0.20. Determine
(i) Amplitude of motion due to the unbalance
(ii)
Transmissibility, and
(iii)
Maximum dynamic force.
A machine and its foundation weigh 160 kN. The spring constant and the damping ratio of the soil
supporting the soil may be taken as 14×104 kN/m and 0.25, respectively. Forced vibration of the
Q(kN )  Qo sin t
foundation is caused by a force that can be expressed as :
Qo  45kN ,   155 rad / s
Determine
(i) The undamped natural frequency of the foundation
(ii) Amplitude of motion, and
(iii) Maximum dynamic force transmitted to the subgrade.