$A$ particle executes harmonic motion with an angular velocity and maximum acceleration of $3.5\, rad/s$ and $7.5\, m/s^2$ respectively. The amplitude of oscillation is .... $m$

$A$ body of mass $0.4 \text{ kg}$ performs simple harmonic motion. It experiences a restoring force of $0.4 \text{ N}$ when its displacement from the mean position is $4 \text{ cm}$. The force constant and magnitude of acceleration respectively are

Write the formula of instantaneous acceleration of $SHM$ particle along $X$-axis.

$A$ piston is performing $S.H.M.$ in the vertical direction with a frequency of $0.5 \,Hz$. $A$ block of $10 \,kg$ is placed on the piston. The maximum amplitude of the system such that the block remains in contact with the piston is: (in $\,m$)

Two simple harmonic motions of angular frequency $100 \, rad \, s^{-1}$ and $1000 \, rad \, s^{-1}$ have the same displacement amplitude. The ratio of their maximum acceleration is

$A$ body is executing $S.H.M.$ under the action of a force having a maximum magnitude of $50 \,N$. When its energy is half kinetic and half potential, the magnitude of the force acting on the particle is: