The time period of oscillations of a simple pendulum is $1$ minute. If its length is increased by $44 \%$. then its new time period of oscillation will be ......... $s$
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A particle execute $S.H.M.$ along a straight line. The amplitude of oscillation is $2 \,cm$. When displacement of particle from the mean position is $1 \,cm$, the magnitude of its acceleration is equal to magnitude of its velocity. The time period of oscillation is ........
A particle is performing $S.H.M.$ with energy of vibration $90 \,J$ and amplitude $6 \,cm$. When the particle reaches at distance $4 \,cm$ from mean position, it is stopped for a moment and then released. The new energy of vibration will be ........... $J$
Let $T_1$ and $T_2$ be the time periods of two springs $A$ and $B$ when a mass $m$ is suspended from them separately. Now both the springs are connected in parallel and same mass $m$ is suspended with them. Now let $T$ be the time period in this position. Then
Two masses $m_1=1 \,kg$ and $m_2=0.5 \,kg$ are suspended together by a massless spring of spring constant $12.5 \,Nm ^{-1}$. When masses are in equilibrium $m_1$ is removed without disturbing the system. New amplitude of oscillation will be .......... $cm$
A uniform spring of force constant $k$ is cut into two pieces, the lengths of which are in the ratio $1 : 2$. The ratio of the force constants of the shorter and the longer pieces is