Simple Harmonic...

A cylindrical piston of mass M slides smoothly inside a long cylinder closed at one end, enclosing a certain mass of gas. The cylinder is kept with its axis horizontal. If the piston is disturbed from its equilibrium position, it oscillates simple harmonically. The period of oscillation will be

One end of a spring of force constant k is fixed to a vertical wall and the other end is connected to a block of mass m resting on a smooth horizontal surface. There is another wall at a distance x₀​ from the body. The spring is now compressed by 3x_0​ and released. The time after which the block will strike the other wall is

Two particles move parallel to x-axis about the origin with same amplitude and frequency. At a certain instant they are found at a distance a/3​ from the origin on opposite sides but their velocities are found to be in same direction.Then the phase difference between two particles will be 

A particle performs SHM with a period T and amplitude a.The mean velocity of the particle over the time interval during which it travels a distance a/2 from the extreme position is

A body is executing SHM, At a displacement x, its potential energy is E₁​ and at a displacement y, its potential energy is E_2​. Find its potential energy E at displacement ( x + y)  

Two identical springs are attached to a small block P. The other ends of the springs are fixed at A and B. When P is in equilibrium the extension of top spring is 20 cm and extension of bottom spring is l0 cm. The period of small vertical oscillations of P about its equilibrium position is (use g = 9.8 m/s₂)

If two simple pendulums first of bob mass M₁​ and length l₁​, second of bob mass M₂​ and length l₂​. Given M₁​=M₂​ and l₁​=2l₂​. If the vibrational energies of both are same, then which of the following is correct ?

A particle is executing a motion in which its displacement as a function of time is given by x = 3sin ⁡(5πt + π/3) + cos ⁡(5πt + π/3) where x is in m and t is in s. Then the motion is 

A particle is subjected to two simple harmonic motions in the same direction having equal amplitudes and equal frequency. If the resultant amplitude is equal to the amplitude of the individual motions. Find the phase difference between the individual motions.

one end of a spring of force constant ′k′ is fixed to a vertical wall and the other to a block of mass ′in′ resting on a smooth horizontal surface. There is another wall at a distance ′x₀′​ from the block. The spring is then compressed by 2x₀​ and released. The time taken by the block to strike the other wall is