When a mass $m$ is attached to a spring it oscillates with period $4 \,s$. When an additional mass of $2 \,kg$ is attached to a spring, time period increases by $1 \,s$. The value of $m$ is ........... $kg$

A clock $S$ is based on oscillations of a spring and a clock $P$ is based on pendulum motion. Both clocks run at the same rate on earth. On a planet having same density as earth but twice the radius then

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 attached to a spring is free to oscillate, with angular velocity $\omega,$ in a hortzontal plane without friction or damping. It is pulled to a distance $x_{0}$ and pushed towards the centre with a velocity $v_{ o }$ at time $t=0 .$ Determine the amplitude of the resulting oscillations in terms of the parameters $\omega, x_{0}$ and $v_{ o } .$ [Hint: Start with the equation $x=a \cos (\omega t+\theta)$ and note that the initial velocity is negative.]

The graph shown was obtained from experimental measurements of the period of oscillations $T$ for different masses $M$ placed in the scale pan on the lower end of the spring balance. The most likely reason for the line not passing through the origin is that the

A mass $m$ attached to a spring oscillates every $2\, sec$. If the mass is increased by $2 \,kg$, then time-period increases by $1\, sec$. The initial mass is ..... $kg$