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 :

The potential energy of a long spring when stretched by $2 \mathrm{cm}$ is $U$. If the spring is stretched by $8 \mathrm{cm}$, potential energy stored in it will be:

The $x-t$ graph of a particle performing simple harmonic motion is shown in the figure. The acceleration of the particle at $t=2 \mathrm{s}$ is:

A particle of mass $m$ oscillates in Simple Harmonic Motion between points $x_1$ and $x_2$, the equilibrium position being $O$. Which of the following graphs represents the variation of its potential energy $\left(U\right)$ with respect to its position?

The $\mathrm{x}-\mathrm{t}$ graph of a particle undergoing simple harmonic motion is as shown in the figure.

The acceleration of the particle at $\mathrm{t}=\frac{4}{3}\mathrm{ }\mathrm{s}$ is

A particle executing SHM with an amplitude $\mathrm{A}$. The displacement of the particle when its potential energy is half of its total energy is

Two particles are performing SHM in same phase. It means that:
 

Graph between velocity and displacement of a particle, executing S.H.M. is

The displacement of a simple harmonic motion of amplitude $6 \mathrm{cm}$ when its kinetic energy is equal to its potential energy is

Thus, simple harmonic motion (SHM) is not any periodic motion but one in which displacement is sinusoidal function of time.

Two SHM’s are respectively by $y=a_1\sin (\omega t-kx)$ and $y=a_2\cos (\omega t-kx).$ The phase difference between the two is

When a spring-mass system vibrates with simple harmonic motion, the mass in motion reaches its maximum velocity when its acceleration is _____ (maximum\minimum).

A block of mass $\mathrm{m}=4 \mathrm{kg}$ undergoes simple harmonic motion with amplitude$\mathrm{A}= 6 \mathrm{cm}$ on the frictionless surface. Block is attached to a spring of force constant $k=400 \mathrm{N} {\mathrm{m}}^{-1}$ . If the block is at$\mathrm{x}=6 \mathrm{cm}$ at time $t=0$ and equilibrium position is at $x=0$ then the blocks position as a function of time (with x in centimetres and t in seconds) ?

A mass of $36 \mathrm{kg}$ is kept vertically on the top of a massless spring. What is the maximum compression of the spring if the spring constant is $15000 \mathrm{N}/\mathrm{m}$. Assume $\mathrm{g} = 10\mathrm{m}/{\mathrm{s}}^2$.

Suppose a particle P is moving uniformly on a circle of radius A with the angular speed $\omega$ . The sense of rotation is anticlockwise. If the $t=0$ , it  makes an angle of $\varphi$ with the positive direction of the x-axis. In time $t$, it will cover a further angle $\omega t$.What is the projection of position vector on the X-axis at time $t$.

If we tie a stone to the end of a string and move it with a constant angular speed in a horizontal plane about fixed point, the stone would perform a : 

If the particle is moving in circular motion under SHM, then its x-projection is depending upon

The x-projection for a certain particle in circular motion under SHM with period of $2 \mathrm{s}$, amplitude of oscillation is $2 \mathrm{m}$ and initial phase of $\frac{\mathrm{\pi }}{2}$ is

Which of the following conditions is not sufficient for S.H.M. and why?

The formula for time period of a compound pendulum is