The potential energy of a particle of mass $4\,kg$ in motion along the $x$-axis is given by $U =4(1-\cos 4 x )\,J$. The time period of the particle for small oscillation $(\sin \theta \simeq \theta)$ is $\left(\frac{\pi}{ K }\right)\,s$. The value of $K$ is .......
JEE MAIN 2022, Diffcult
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1A plank with a small block on top of it is under going vertical $SHM$ . Its period is $2\ sec$ . The minimum amplitude at which the block will separate from plank isView Solution
- 2A loaded vertical spring executes $S.H.M.$ with a time period of $4\; sec$. The difference between the kinetic energy and potential energy of this system varies with a period of ........$sec$View Solution
- 3The equation of motion of a particle of mass $1\,g$ is $\frac{{{d^2}x}}{{d{t^2}}} + {\pi ^2}x = 0$ where $x$ is displacement (in $m$ ) from mean position. The frequency of oscillation is .... $s$ (in $Hz$ )View Solution
- 4Two bodies performing $SHM$ have same amplitude and frequency. Their phases at a certain instant are as shown in the figure. The phase difference between them isView Solution
- 5View SolutionThe total energy of a particle executing S.H.M. is proportional to
- 6The displacement of a particle is represented by the equation $y = sin^3\,\,\,\omega t$ . The motion isView Solution
- 7A particle executes $S.H.M.$ of amplitude A along $x$-axis. At $t =0$, the position of the particle is $x=\frac{A}{2}$ and it moves along positive $x$-axis the displacement of particle in time $t$ is $x=A \sin (\omega t+\delta)$, then the value $\delta$ will beView Solution
- 8A pendulum has time period $T$. If it is taken on to another planet having acceleration due to gravity half and mass $ 9 $ times that of the earth then its time period on the other planet will beView Solution
- 9A particle executes simple harmonic motion with an amplitude of $5\, cm$. When the particle is at $4\, cm$ from the mean position, the magnitude of its velocity is $SI\,units$ is equal to that of its acceleration. Then, its periodic time in seconds isView Solution
- 10A pendulum clock that keeps correct time on the earth is taken to the moon it will run (it is given that $g_{Moon} = g_{Earth}/6$ )View Solution