1. A flywheel weighing 70 lb was allowed to swing as a pendulum about a knife-edge at the inner side of the rim, as shown in the figure. If the measured period of oscillation was 1.22 s, determine the moment of inertia of the flywheel about its geometric axis.
2. A uniform bar of radius of gyration k about its centre of gravity is suspended hori- zontally by two vertical strings of length h, at distances a and b from the mass centre. Prove that the bar will oscillate about the vertical line thro ugh the mass centre, and q determine the frequency of oscillation.
3. A rigid bar (assumed massless) is hinged at its left end and supports a lumped mass m. Write the differential equation governing the motion of the system and determine the natural frequency of damped oscillation and the critical damping coefficient.
4. A spring-mass system with viscous damping is displaced from its equilibrium position and released from rest. If the amplitude of oscillation diminished by 5% each cycle, de- termine the fraction of critical damping included in the system
5. A rigid uniform bar of mass m and length l is pinned at O and supported by a spring and a viscous damper as shown. Measuring the angular displacement of the bar θ from the equilibrium position, determine:(a) the governing differential equation for small angles;(b) the equation for the undamped natural frequency; and (c) the expression for critical damping.
6. A piston of mass 4.53 kg is travelling in a tube with a velocity of 15.24 m/s and en- gages a spring and damper, as shown below. Determine the maximum displacement of the piston after engaging the spring-damper. How many seconds does it take?