Two bodies of masses $1 \mathrm{kg}$ and $4 \mathrm{kg}$ are connected to a vertical spring, as shown in the figure. The smaller mass executes simple harmonic motion of angular frequency $25 \mathrm{rad} {\mathrm{s}}^{-1}$, and amplitude $1.6 \mathrm{cm}$ while the bigger mass remains stationary on the ground. The maximum force exerted by the system on the floor is (take $g = 10 \mathrm{m} {\mathrm{s}}^{-2}$).

The amplitude of a simple pendulum, oscillating in air with a small spherical bob, decreases from 10 cm to 8 cm in 40 seconds. Assuming that Stokes law is valid, and ratio of the coefficient of viscosity of air to that of carbon dioxide is 1.3, the time in which amplitude of this pendulum will reduce from 10 cm to 5 cm in carbondioxide will be close to (ln 5 = 1.601, ln 2 = 0.693).

An ideal gas enclosed in a vertical cylindrical container supports a freely moving piston of mass $\mathit{\text{M}}$. The piston and the cylinder have equal cross-sectional area $\mathit{\text{A}}$. When the piston is in equilibrium, the volume of the gas is $V_0$ and its pressure is $M_0$. The piston is slightly displaced from the equilibrium position and released. Assuming that the system is completely isolated from its surrounding, the piston executes a simple harmonic motion with frequency
[Assume the system is in space.]