A block is placed on a horizontal plank. The plank is performing $SHM$ along a vertical line with amplitude of $40\,cm.$ The block just loses contact with the plank when the plank is momentarily at rest. Then :
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A uniform rod of length $2.0 \,m$ is suspended through an end and is set into oscillation with small amplitude under gravity. The time period of oscillation is approximately .... $\sec$
A particle of mass $m$ moves in a one-dimensional potential energy $U(x) = -ax^2 + bx^4,$ where $'a'$ and $'b'$ are positive constants. The angular frequency of small oscillations about the minima of the potential energy is equal to
A simple pendulum with iron bob has a time period $T$. The bob is now immersed in a non-viscous liquid and oscillated. If the density of liquid is $\frac{1}{12}$ th that of iron, then new time period will be
Two massless springs with spring constants $2\,k$ and $2\,k$, carry $50\, g$ and $100 \,g$ masses at their free ends. These two masses oscillate vertically such that their maximum velocities are equal. Then, the ratio of their respective amplitudes will be
The period of a simple pendulum, whose bob is a hollow metallic sphere, is $T$.The period is $T_1$ when the bob is filled with sand, $T_2$ when it is filled with mercury and $T_3$ when it is half filled with mercury. Which of the following is true