Frequency of a simple pendulum in a freely falling lift is

A point performs simple harmonic oscillation of period T and the equation of motion is given by
After the elapse of what fraction of the time period the velocity of the point will be equal to half of its maximum velocity ?

In a simple harmonic motion, if the displacement is half of the amplitude, then which part of total energy will be kinetic energy ?

A wave has SHM (simple harmonic motion) whose period is 4 s while another wave which also possesses SHM has its period 3 s.  If both are combined, then the resultant wave will have the period equal to

A particle is performing simple harmonic motion along x axis with amplitude 4 cm and time period 1.2 sec.  The minimum time taken by the particle to move from x = + 2 cm to x = + 4 cm and back again is

A mass of 2.0 kg is put on a flat pan attached to a vertical spring fixed on the ground as shown in the figure.  The mass of the spring and the pan is negligible.  When pressed slightly and released the mass executes a simple harmonic motion.  The spring constant is 200 N/m.  What should be the minimum amplitude of the motion, so that the mass gets detached from the pan ?
(Take g =10m/s² )

A simple pendulum is executing simple harmonic motion with a time period T.  If the length of the pendulum is increased by 21%, the increase in the time period is

Two simple pendulums having lengths 0.5 m and 2.0 m are displaced linearly a little at the same time.  They will be in the same phase when shorter pendulum completes oscillations equal to

The total energy of a body performing S.H.M. depends on

A simple pendulum with a bob of mass m oscillates from A to C and back to A [See Fig.25.26] such that PB is H.  If the acceleration due to gravity is g then velocity of the bob as it passes through B is