problem 1) prepare brief notes on:

(a) State degree of freedom of a vibratory system.

(b) What parameters are essential so that vibration may occur?

(c) How do you add two harmonic motions having different frequencies?

(d) State critical damping and its importance in vibrating system.

(e) In a spring mass system, if the mass of the system is doubled with spring stiffness halfed, the natural frequency of longitudinal vibrations will be ................ .

(f) What is orthogonality principle?

(g) List of the various types of damping.

(h) What do you understand by torsionally equivalent shafts?

(i) prepare down the difference between continuous and discrete systems?

(j) State the flexibility and stiffness influence coefficients.

problem 2) A body of 5 kg is supported on the spring of stiffness 200 N/m and has a dashpot connected to it which produces a resistance of 0.002 N at a velocity of 1 cm/sec. In what ratio the amplitude of vibration is reduced after 5 seconds?

problem 3) Diesel engine of the single cylinder has a mass of 500 kg and is mounted on mild steel chassis frame. The static deflection due to weight of chassis is 2.5 mm. The reciprocating masses of the engine amounts to 20 kg and the stroke of the engine is 180 mm. A dash pot with a damping coefficient of 2000 N.S/m is also used to dampen the vibrations. In the steady state of vibrations, find out the amplitude of the vibrations if the driving shaft rotates at 400 r.p.m

problem 4) A bar fixed at one end is pulled at the other end with a force P. The force is suddenly released. Investigate the vibrations of the bar.

problem 5) Derive appropriate expression for longitudinal vibrations for the rectangular uniform cross-sectional bar of length l fixed at one end and free it other end.