Define and explain the terminologies used in vibration.

A body is subjected to two harmonic motions as given below:
x1 10 sin (wt and
x2 8 cos (wt
What harmonic motions should be given to the body to bring it to equilibrium?

2. A mass of 1 kg is to be supported on a spring having a stiffness of 9800 N/m. The damping coefficient is 5·9 N-s/m. Determine the natural frequency of the system. Also find the logarithmic decrement and the amplitude after 3 cycles, if the initial displacement is 0·3 cm.

3. A spring-mass system shown in Figure 1 is subjected to a harmonic force F cos rot. Determine the response of the system.
Given
0.01 m
0.04 m/sec
w 30 rad/sec
F 1000 N
m =10 kg
k =500 N/m

<img src='./qimages/15750-3.jpg'>

4. Explain any three of the following:

Logarithmic decrement

Critical damping

Vibration isolation

Equivalent stiffness of spring in series and in parallel

Derive the governing equation of single degree spring-mass damped system under harmonic excitation, using D'Alembert's principle.

Determine the steady state response of the system described in part for harmonic excitation with fixed amplitude.

A spring-mass system has a period 0·25 sec. What will be the new period, if spring constant is increased by 50%

A vibratory system in a vehicle is to be designed with the following parameters:
k 110 c 2 m 1.1 kg.

Calculate

the decrease of starting value oscillations, amplitude after from its complete

the frequency of oscillations.

Explain torsionally equivalent shaft.

Find the natural frequencies and mode shape for the system shown in Figure 2.

<img src='./qimages/15750-7b.jpg'>

I1 10 kg-m^2
12 40 kg-m^2
kt1 kt2 kt3 15 N-m/radian