Oscillations Te...

Two masses m₁ and m₂ are suspended together by a massless spring of constant K. When the masses are in equilibrium, m₁ is removed without disturbing the system. Then the angular frequency of oscillation of m₂ is

Two light springs of force constants k₁ and k₂ (each 3.2 N m^–1) and a block of mass ‘m’ (=200 g) are in one line AB on a smooth horizontal table such that one end of each spring is fixed on a rigid support and the other end is free as shown in Fig. 10.16. The distance CD between the free ends of a spring is 60.0 cm. If block moves along AB with a velocity 120 cm in between the springs, the period of oscillations of the block is

On a smooth inclined plane, a body of mass M is attached between two springs. The other ends of the springs are fixed to firm support. If each spring has force constant k, the period of oscillation of he body (assuming the springs as massless) is

Masses m and 3 m are attached to the two ends of a spring of constant k. If the system vibrates freely, the period of oscillation will be

If X, F and U denote the displacement, force acting on and potential energy of a particle, then

For a particle executing simple harmonic motion, the kinetic energy K at an instant t is given by K = K₀ cos² wt
The maximum value of potential energy is

A body performs S.H.M. Its kinetic energy K, varies with time t, as indicated in graph

The work done by the string of a simple pendulum during one complete oscillation is equal to

A particle starts S.H.M. from the mean position. Its amplitude is a and total energy E. At one instant its kinetic energy is 3 E/4 its displacement at this instant is

For a particle executing S.H.M., the kinetic energy k is given by k₀ cos²wt. The maximum value of potential energy is