Practice problems Set-3 (Harmonically excited vibration)
Questions from SS Rao, Mechanical Vibration, Pearson, 4e. (Chapter 3)
1. In the cam-follower system shown in Figure, the rotation of the cam imparts a vertical
motion to the follower. The pushrod, which acts as a spring, has been compressed by
an amount before assembly. Determine the following: (a) equation of motion of the
follower, including the gravitational force; (b) force exerted on the follower by the cam;
and (c) conditions under which the follower loses contact with the cam.
2. Derive the equation of motion and find the steady-state response of the system shown in
Figure for rotational motion about the hinge O for the following data:
k1 = k2 = 5000 N/m, a = 0.25 m, b = 0.5 m, l = 1 m, M = 50 kg, m = 10 kg, F0 = 500 N, Excitation
frequency ω = 1000 rpm.
3. A spring-mass-damper system is subjected to a harmonic force. The amplitude is found to be
20 mm at resonance and 10 mm at a frequency 0.75 times the resonant frequency. Find the
damping ratio of the system.
4. For the system shown in Figure, x and y denote, respectively, the absolute displacements of
the mass m and the end Q of the dashpot (a) Derive the equation of motion of the mass m, (b)
find the steady-state displacement of the mass m, and (c) find the force transmitted to the
support at P, when the end Q is subjected to the harmonic motion y(t) = Y cos ωt.
5. The propeller of a ship, of weight 105 N and polar mass moment of inertia 10,000 kg-m2 is
connected to the engine through a hollow stepped steel propeller shaft, as shown in Figure.
Assuming that water provides a viscous damping ratio of 0.1, determine the torsional vibratory
response of the propeller when the engine induces a harmonic angular displacement of
0.05sin314.16t rad at the base (point A) of the propeller shaft.