The time period of a bob performing simple harmonic motion in water is $2 \mathrm{s}$. If density of bob is $\frac{4}{3}\times {10}^3 \mathrm{kg} {\mathrm{m}}^{-3}$, then time period of bob performing simple harmonic motion in air will be

A body of mass $1 \mathrm{kg}$ is executing simple harmonic motion. Its displacement $y\left(\mathrm{cm}\right)$ at $t$ seconds is given by $y=6\sin \left(100t+\frac{\pi }{4}\right)$. Its maximum kinetic energy is

A load of mass $m$ falls from a height $h$ on the scale pan hung from a spring as shown. If the spring constant is $k$ and the mass of the scale pan is zero and the mass $m$ does not bounce relative to the pan, then the amplitude of vibration is