Show that a simple pendulum executes S.H.M. when the angular displacement is small.

Time period of a particle in SHM depends on the force constant k and mass m of the particle as follows: T=2pisqrt(m/k) . A simple pendulum executes SHM approximately, why then is the time period of a simple pendulum independent of the mass of the pendulum?

How will the time period of a simple pendulum change when its length is doubled?

A wheel has angular acceleration of 2.0 rad. s^(-2) and an initial angular speed of 1.0 rad .s^(-1) . What will be the angular displacement (in radian) in 2 s ?

The bob of a simple pendulum executes simple harmonic motion in water with a period T, while the period of oscillation of the bob is T_(0) in air. Neglecting frictional force of water and given that the density of the bob is 4/3xx10^(3)kg*m^(-3) . Prove that, T=2T_(0) .

A particle is moving along a circular path of radius 2 m with constant angular velocity of 3 rad cdot s^(-1) . Detemine the angular displacement (in rad) of the particle in 3 s.