A spring is stretched by $0.20\, m$, when a mass of $0.50\, kg$ is suspended. When a mass of $0.25\, kg$ is suspended, then its period of oscillation will be .... $\sec$   $(g = 10\,m/{s^2})$

A mass $m =100\, gms$ is attached at the end of a light spring which oscillates on a frictionless horizontal table with an amplitude equal to $0.16$ metre and time period equal to $2 \,sec$. Initially the mass is released from rest at $t = 0$ and displacement $x = - 0.16$ metre. The expression for the displacement of the mass at any time $t$ is

The period of oscillation of a mass $M$ suspended from a spring of negligible mass is $T$. If along with it another mass $M$ is also suspended, the period of oscillation will now be

A uniform cylinder of length $L$ and mass $M$ having cross-sectional area $A$ is suspended, with its length vertical, from a fixed point by a massless spring, such that it is half submerged in a liquid of density $\sigma $ at equilibrium position. When the cylinder is given a downward push and released, it starts oscillating vertically with a small amplitude. The time period $T$ of the oscillations of the cylinder will be

A mass $m$ is suspended from the two coupled springs connected in series. The force constant for springs are ${K_1}$ and ${K_2}$. The time period of the suspended mass will be

$Assertion :$ The time-period of pendulum, on a satellite orbiting the earth is infinity.
$Reason :$ Time-period of a pendulum is inversely proportional to $\sqrt g$