A particle of mass $200 \,gm$ executes $S.H.M.$ The restoring force is provided by a spring of force constant $80 \,N / m$. The time period of oscillations is …. $\sec$

A body executes simple harmonic motion under the action of a force $F_1$ with a time period $(4/5)\, sec$. If the force is changed to $F_2$ it executes $SHM$ with time period $(3/5)\, sec$. If both the forces $F_1$ and $F_2$ act simultaneously in the same direction on the body, its time period (in $seconds$ ) is

A man weighing $60\  kg$ stands on the horizontal platform of a spring balance. The platform starts executing simple harmonic motion of amplitude $0.1\  m$ and frequency $\frac{2}{\pi } Hz$. Which of the following staements is correct

A mass $M$ is suspended by two springs of force constants $K_1$ and $K_2$ respectively as shown in the diagram. The total elongation (stretch) of the two springs is

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