A mass $M$ is suspended from a light spring. An additional mass m added displaces the spring further by a distance $x$. Now the combined mass will oscillate on the spring with period
$T = 2\pi \sqrt {\left( {mg/x(M + m)} \right)} $
$T = 2\pi \sqrt {\left( {(M + m)x/mg} \right)} $
$T = (\pi /2)\sqrt {\left( {mg/x(M + m)} \right)} $
$T = 2\pi \sqrt {\left( {(M + m)/mgx} \right)} $
A block of mass $m$ attached to massless spring is performing oscillatory motion of amplitude $'A'$ on a frictionless horizontal plane. If half of the mass of the block breaks off when it is passing through its equilibrium point, the amplitude of oscillation for the remaining system become $fA.$ The value of $f$ is
A $2\, Kg$ block moving with $10\, m/s$ strikes a spring of constant $\pi ^2 N/m$ attached to $2\, Kg$ block at rest kept on a smooth floor, the velocity of the rear $2\, kg$ block after it separates from the spring will be ..... $m/s$
A block of mass $m$ hangs from three springs having same spring constant $k$. If the mass is slightly displaced downwards, the time period of oscillation will be
A mass of $2\,kg$ is attached to the spring of spring constant $50 \,Nm^{-1}$. The block is pulled to a distance of $5 \,cm $ from its equilibrium position at $x= 0$ on a horizontal frictionless surface from rest at $t = 0$. Write the expression for its displacement at anytime $t$.
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 .... $\sec$