A block of mass $m$ is attached to two springs of spring constants $k_1$ and $k_2$ as shown in figure. The block is displaced by $x$ towards right and released. The velocity of the block when it is at $x/2$ will be
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A bar of mass $m$ is suspended horizontally on two vertical springs of spring constant $k$ and $3k$ . The bar bounces up and down while remaining horizontal. Find the time period of oscillation of the bar (Neglect mass of springs and friction everywhere).
A mass $M$, attached to a horizontal spring, executes S.H.M. with amplitude $A_1$. When the mass $M$ passes through its mean position then a smaller mass $m$ is placed over it and both of them move together with amplitude $A_2$. The ratio of $\frac{{{A_1}}}{{{A_2}}}$ is
Time period of a particle executing $SHM$ is $8\, sec.$ At $t = 0$ it is at the mean position. The ratio of the distance covered by the particle in the $1^{st}$ second to the $2^{nd}$ second is :
A simple pendulum, suspended from the ceiling of a stationary van, has time period $T$. If the van starts moving with a uniform velocity the period of the pendulum will be
Two masses ${m_1}$ and ${m_2}$ are suspended together by a massless spring of constant k. When the masses are in equilibrium, ${m_1}$ is removed without disturbing the system. Then the angular frequency of oscillation of ${m_2}$ is
A particle performs $S.H.M.$ of amplitude $A$ with angular frequency $\omega$ along a straight line. Whenit is at a distance $\frac{{\sqrt 3 }}{2}$ $A$ from mean position, its kinetic energy gets increased by an amount $\frac{1}{2}m{\omega ^2}{A^2}$ due to an impulsive force. Then its new amplitude becomes
Two particles are executing S.H.M. The equation of their motion are ${y_1} = 10\sin \left( {\omega \,t + \frac{{\pi T}}{4}} \right),$ ${y_2} = 25\sin \,\left( {\omega \,t + \frac{{\sqrt 3 \pi T}}{4}} \right)$. What is the ratio of their amplitude
For a particle executing $S.H.M.$ the displacement $x$ is given by $x = A\cos \omega t$. Identify the graph which represents the variation of potential energy $(P.E.)$ as a function of time $t$ and displacement $x$