Find the time period of the motion of the particle shown in figure (12-E14). Neglect the small effect of the bend near the bottom.

A 1 kg block is executing simple harmonic motion of amplitude 0.1 m on a smooth horizontal surface under the restoring force of a spring of spring constant 100 N m^-1. A block of mass 3 kg is gently placed on it at the instant it passes through the mean position. Assuming that the two blocks move together find the frequency and the amplitude of the motion.

The left block in figure (12-E13) moves at a speed u towards the right block placed in equilibrium. All collisions to take place are elastic and the surfaces are frictionless. Show that the motions of the two blocks are periodic. Find the time period of these periodic motions. Neglect the widths of the blocks.

All the surfaces shown in figure (12-E15) are frictionless. The mass of the car is M, that of the block is m and the spring has spring constant k. Initially, the car and the block are at rest and the spring is stretched through a length x when the system is released. (a) Find the amplitudes of the simple harmonic motion of the block and of the car as seen from the road. (b) Find the time period(s) of the two simple harmonic motions.

A uniform plate of mass M stays horizontally and symmetrically on two wheels rotating in opposite directions (figure 12-E16). The separation between the wheels is L. The friction coefficient between each wheel and the plate is t. Find the time period of oscillation of the plate if it is slightly displaced along its length and released.