A particle performs S.H.M. with amplitude 'A'. The speed of the particle is $\left(\frac{1}{3}\right)^{\text {rd }}$ of the maximum speed when its displacement from the mean position is

A particle vibrating simple harmonically has an acceleration of $16 \mathrm{~cm} / \mathrm{s}^2$, when it is at a distance of 4 cm from the mean position. Its periodic time is

The average velocity of a particle performing S.H.M. in one complete vibration is ( $\mathrm{A}=$ amplitude of S.H.M., $\omega=$ angular velocity)

A mass ' $M$ ' is suspended from a spring of negligible mass. The spring is pulled a little and then released so that the mass executes S.H.M. of periodic time ' $T$ '. If the mass is increased by ' $m$ ', the time period becomes $4 T / 3$, then the ratio of $\frac{\mathrm{M}}{\mathrm{m}}$ is