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The variation of displacement with time of a particle executing free simple harmonic motion is shown in the figure. The potential energy ${U}({x})$ versus time $({t})$ plot of the particle is correctly shown in figure:
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 simple pendulum is set up in a trolley which moves to the right with an acceleration a on a horizontal plane. Then the thread of the pendulum in the mean position makes an angle $\theta $ with the vertical
An object of mass $0.2 \mathrm{~kg}$ executes simple harmonic motion along $\mathrm{x}$ axis with frequency of $\left(\frac{25}{\pi}\right) \mathrm{Hz}$. At the position $\mathrm{x}=0.04 \mathrm{~m}$ the object has kinetic energy $0.5 \mathrm{~J}$ and potential energy $0.4 \mathrm{~J}$ The amplitude of oscillation is ............ cm.
An ideal gas enclosed in a vertical cylindrical container supports a freely moving piston of mass $M$. The piston and the cylinder have equal cross sectional area $A$. When the piston is in equilibrium, the volume of the gas is $V_0$ and its pressure is $P_ 0$. The piston is slightly displaced from the equilibrium position and released. Assuming that the system is completely isolated from its surrounding, the piston executes a simple harmonic motion with frequency
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 .... $\sec$
Vertical displacement of a plank with a body of mass $'m'$ on it is varying according to law $y = \sin \omega t + \cos \omega t.$ The minimum value of $\omega $ for which the mass just breaks off the plank and the moment it occurs first after $t = 0$ are given by : ( $y$ is positive vertically upwards)
A cuboidal piece of wood has dimensions $a, b$ and $c$. Its relative density is $d$. It is floating in a large body of water such that side a is vertical. It is pushed down a bit and released. The time period of $SHM$ executed by it is :
A simple pendulum is attached to the roof of a lift. If time period of oscillation, when the lift is stationary is $T$. Then frequency of oscillation, when the lift falls freely, will be
Three masses $700g, 500g$, and $400g$ are suspended at the end of a spring a shown and are in equilibrium. When the $700g$ mass is removed, the system oscillates with a period of $3$ seconds, when the $500 \,gm$ mass is also removed, it will oscillate with a period of ...... $s$