Problem 1: A mass of 0.5 kg is suspended from a flywheel as shown in Figure. If the mass is released from rest and falls a distance of 0.5 m in 1.5 s, calculate:

a. The linear acceleration of the mass.

b. The angular acceleration of the wheel.

c. The tension in the rope.

d. The frictional torque, resisting motion.

Problem 2: A mass of 0.3 kg is suspended from a spring of stiffness 200 N m-1. If the mass is displaced by 10 mm from its equilibrium position and released, for the resulting vibration, calculate:

(a) (i) the frequency of vibration

(ii) the maximum velocity of the mass during the vibration

(iii) the maximum acceleration of the mass during the vibration

(iv) the mass required to produce double the maximum velocity calculated in (ii) using the same spring and initial deflection.

(b) Plot a graph of acceleration against displacement (x) (for values of x from x = -10 mm to x = +10 mm)