There is a simple pendulum hanging from the ceiling of a lift. When the lift is stand still, the time period of the pendulum is $T$. If the resultant acceleration becomes $g/4,$ then the new time period of the pendulum is
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The kinetic energy of a particle executing $S.H.M.$ is $16\, J$ when it is in its mean position. If the amplitude of oscillations is $25\, cm$ and the mass of the particle is $5.12\, kg$, the time period of its oscillation is
A cylindrical block of wood (density $= 650\, kg\, m^{-3}$), of base area $30\,cm^2$ and height $54\, cm$, floats in a liquid of density $900\, kg\, m^{-3}$ . The block is depressed slightly and then released. The time period of the resulting oscillations of the block would be equal to that of a simple pendulum of length ..... $cm$ (nearly)
A particle which is simultaneously subjected to two perpendicular simple harmonic motions represented by; $x = {a_1}\,\cos \,\omega t$ and $y = {a_2}\,\cos \,2\,\omega t$ traces a curve given by
A particle executes simple harmonic motion with an amplitude of $4 \,cm$. At the mean position the velocity of the particle is $10\, cm/s$. The distance of the particle from the mean position when its speed becomes $5 \,cm/s$ is