The displacement of a particle varies with time as $x = 12\sin \omega t - 16{\sin ^3}\omega t$ (in $cm$). If its motion is $S.H.M.$, then its maximum acceleration is
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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 $1.00 \times {10^{ - 20}}kg$ particle is vibrating with simple harmonic motion with a period of $1.00 \times {10^{ - 5}}sec$ and a maximum speed of $1.00 \times {10^3}m/s$. The maximum displacement of the particle is
A sphere of radius $r$ is kept on a concave mirror of radius of curvature $R$. The arrangement is kept on a horizontal table (the surface of concave mirror is frictionless and sliding not rolling). If the sphere is displaced from its equilibrium position and left, then it executes $S.H.M.$ The period of oscillation will be
Two identical spring of constant $K$ are connected in series and parallel as shown in figure. A mass $m$ is suspended from them. The ratio of their frequencies of vertical oscillations will be
The potential energy of a simple harmonic oscillator at mean position is $2\,joules$. If its mean $K.E.$ is $4\,joules$, its total energy will be .... $J$
Two bodies performing $SHM$ have same amplitude and frequency. Their phases at a certain instant are as shown in the figure. The phase difference between them is