A particle of mass $m$ in a unidirectional potential field have potential energy $U(x)=\alpha+2 \beta x^2$, where $\alpha$ and $\beta$ are positive constants. Find its time period of oscillation.
Medium
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 body is executing simple harmonic motion of amplitude $a$ and period $T$ about the equilibrium position $x=0$. Large numbers of snapshots are taken at random of this body in motion. The probability of the body being found in a very small interval $x$ to $x+|d x|$ is highest atView Solution
- 2The length of a simple pendulum is increased by $2\%$. Its time period willView Solution
- 3Two independent harmonic oscillators of equal mass are oscillating about the origin with angular frequencies $\omega_1$ and $\omega_2$ and have total energies $E_1$ and $E_2$, respectively. The variations of their momenta $p$ with positions $x$ are shown in the figures. If $\frac{a}{b}= n ^2$ and $\frac{ a }{ R }= n$, then the correct equation$(s)$ is(are) $Image$View Solution
$(A)$ $E_1 \omega_1=E_2 \omega_2$ $(B)$ $\frac{\omega_2}{\omega_1}=n^2$ $(C)$ $\omega_1 \omega_2= n ^2$ $(D)$ $\frac{E_1}{\omega_1}=\frac{E_2}{\omega_2}$
- 4Two particles are executing simple harmonic motion of the same amplitude $A$ and frequency $\omega $ along the $x-$ axis. Their mean position is separated by distance $X_0 (X_0> A)$. If the maximum separation between them is $(X_0 +A)$, the phase difference between their motion isView Solution
- 5Two simple harmonic motions are represented by the equations $x_{1}=5 \sin \left(2 \pi t+\frac{\pi}{4}\right), x_{2}=5 \sqrt{2}(\sin 2 \pi t+\cos 2 \pi t)$ The ratio of the amplitude of $x_{1}$ and $x_{2}$ isView Solution
- 6A particle is executing Simple Harmonic Motion $(SHM)$. The ratio of potential energy and kinetic energy of the particle when its displacement is half of its amplitude will beView Solution
- 7A heavy small-sized sphere is suspended by a string of length $l$. The sphere rotates uniformly in a horizontal circle with the string making an angle $\theta $ with the vertical. Then the time period of this conical pendulum isView Solution
- 8Figure shows the circular motion of a particle. The radius of the circle, the period, sense of revolution and the initial position are indicated on the figure. The simple harmonic motion of the $x-$ projection of the radius vector of the rotating particle $P$ isView Solution
- 9Starting from the mean position a body oscillates simple harmonically with a period of $2\,s.$ After what time will its kinetic energy be $75\%$ of the total energy ?View Solution
- 10A body of mass $0.01 kg$ executes simple harmonic motion $(S.H.M.)$ about $x = 0$ under the influence of a force shown below : The period of the $S.H.M.$ is .... $s$View Solution
