For a particle performing $S.H.M.$, the displacement-time graph is shown. For that particle, the force-time graph is correctly represented by which of the following?

$A$ simple harmonic oscillator has an amplitude of $0.5 \ m$ and a time period of $2 \ s$. What is the magnitude of acceleration when it is displaced from the mean position by $0.25 \ m$?

For a particle performing Simple Harmonic Motion $(S.H.M.)$,the displacement-time graph is as shown. For that particle,the force-time graph is correctly represented by which of the following graphs?

The acceleration of a particle performing $S.H.M.$ at a distance of $3\;cm$ from the mean position is $12\;cm/s^2$. Its time period is ..... $s$.

$A$ particle of mass $10 \,g$ is undergoing $S.H.M.$ with an amplitude of $10 \,cm$ and a period of $0.1 \,s$. The maximum value of the force on the particle is about ............ $N$.

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