A mass hangs from a spring and oscillates vertically. The top end of the spring is attached to the top of a box, and the box is placed on a scale, as shown in the figure. The reading on the scale is largest when the mass is
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In the given figure, a mass $M$ is attached to a horizontal spring which is fixed on one side to a rigid support. The spring constant of the spring is $k$. The mass oscillates on a frictionless surface with time period $T$ and amplitude $A$. When the mass is in equilibrium position, as shown in the figure, another mass $m$ is gently fixed upon it. The new amplitude of oscillation will be
The displacement of a particle varies with time as $x = 12\sin \omega t - 16{\sin ^3}\omega t$ (in $cm$). If its motion is $S.H.M.$, then its maximum acceleration is
A body oscillates with $S.H.M.$ according to the equation $x=(5.0 \,m ) \cos \left[\left(2 \pi \,rad s ^{-1}\right) t+\pi / 4\right]$ At $t=1.5 \,s$, its acceleration is ....... $m / s ^2$
The metallic bob of a simple pendulum has the relative density $\rho$. The time period of this pendulum is $T$. If the metallic bob is immersed in water, then the new time period is given by
A particle is executing $S.H.M.$ with time period $T^{\prime}$. If time period of its total mechanical energy is $T$ then $\frac{T^{\prime}}{T}$ is ........
Two, spring $P$ and $Q$ of force constants $k_p$ and ${k_Q}\left( {{k_Q} = \frac{{{k_p}}}{2}} \right)$ are stretched by applying forces of equal magnitude. If the energy stored in $Q$ is $E$, then the energy stored in $P$ is