Simple Harmonic Motion

Electrons moving with different speeds enter a uniform magnetic field in a direction perpendicular field. They will move along circular paths, time periods of rotation will be :

Figure shows the graph of velocity versus displacement of particle executing simple harmonic motion. The frequency of oscillation of the particle will be

Calculate the value of '$\mathrm{g}$' at a place where a simple pendulum of length $2.25 \mathrm{m}$ has time period $T=3 \mathrm{s}$ (Take ${\pi }^2=9.87$).

If $y=A\sin \left(kx-\omega t\right)$, then find $\frac{{\displaystyle \frac{dy}{dx}}}{{\displaystyle \frac{dy}{dt}}}$.

The velocity of a particle, executing S.H.M, is at its mean position.

Two waves represented by equations $y_1=asin\left(\omega t-kx\right)$ and $y_2=a\sin \left(\omega t-kx+\frac{\pi }{2}\right)$ respectively are superimposed. The initial phase of the resultant wave at $x=0$ will be (symbols have their usual meanings)

For a particle showing motion under the $F=-5{\left(x-2\right)}^2$, the motion is

The displacements of two particles executing SHM on the same line are given $y_1=a\sin \left(\frac{\pi }{2}t+\varphi \right)$ and $y_2=b\sin \left(\frac{2\pi }{3}t+\varphi \right)$. The phase difference between them at $t=1 \mathrm{s}$ is

The frequency of note P is $2$ times that of note Q. The energy of both notes is $4:1$. Then amplitude ratio of note of P to note of Q.

The displacement of two particles executing S.H.M are represented by $y_1=a\sin \omega t$ and $y_2=a\cos \left(\omega t+\varphi \right)$. The phase difference between the velocities of these particles is

In a simple harmonic oscillation, the shape of acceleration against displacement for one complete oscillation will be

In the figure shown two motors $P_1 \& P_2$ fixed on a plank which is hanging with light string passing over fixed Pulley $P$. If the motors starts winding the thread with angular velocity ${\omega }_1$ & ${\omega }_2$ then velocity of plank $V$ is (here $R_1 \& R_2$ are the radii of motor rotor respectively) [Given: ${\omega }_1=2 \mathrm{rad} {\mathrm{s}}^{-1}, R_1=2 \mathrm{m}, {\omega }_2=2 \mathrm{rad} {\mathrm{s}}^{-1}, R_2=3 \mathrm{m}$]

The potential energy of a particle performing SHM is given by $U=\frac{1}{2}k{A}^2{\sin }^2\left(\omega t\right)$. Which one of the following options correctly represents the graph for potential energy vs. time?

Which one of the following is the correct acceleration vs. time graph for a particle performing SHM?

Which one of the following is the correct graph for acceleration vs. displacement of a particle performing SHM?

The shape of velocity vs. time graph for a particle performing SHM is

Which one of the following pair of particles are having opposite phase?

Which one of the following pair of particles performing SHM are in phase with each other?

Total energy of a body in Simple harmonic motion depends on

A particle performs simple harmonic motion. A large number of snapshots of its position are taken at random. A histogram of these positions will