A particle is vibrating in S.H.M. with an amplitude of $$4 \mathrm{~cm}$$. At what displacement from the equilibrium position is its energy half potential and half kinetic?

A rubber ball filled with water, having a small hole is used as the bob of a simple pendulum. The time period of such a pendulum

The maximum velocity of a particle performing S.H.M. is '$$\mathrm{V}$$'. If the periodic time is made $$\left(\frac{1}{3}\right)^d$$ and the amplitude is doubled, then the new maximum velocity of the particle will be

A child is sitting on a swing which performs S.H.M. It has minimum and maximum heights from ground $$0.75 \mathrm{~cm}$$ and $$2 \mathrm{~m}$$ respectively. Its maximum speed will be $$\left[\mathrm{g}=10 \frac{\mathrm{m}}{\mathrm{s}^2}\right]$$