$A$ 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 ............ $N$.

The maximum force acting on a particle executing simple harmonic motion is $10 \,N$. The force on the particle when it is midway between mean and extreme positions will be

$A$ man of mass $M$ is standing on a platform. The platform is executing $S.H.M.$ of frequency $f$ in the vertical direction. The span of oscillation is $L$. What is the acceleration of the platform at the top of the oscillation?

$A$ particle vibrating simple harmonically has an acceleration of $16 \ cm/s^2$ when it is at a distance of $4 \ cm$ from the mean position. Its time period is: (in $s$)

$A$ book is resting on a shelf that is undergoing vertical simple harmonic oscillations with an amplitude of $2.5 \,cm$. What is the minimum frequency of oscillation of the shelf for which the book will lose contact with the shelf (in $,Hz$)? (Assume that $g = 10 \,m/s^2$)

Obtain the force law for $SHM$ from the displacement of $SHM$ particle.