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 :

In SHM $\mathrm{X}=\sqrt{2}\sin \left(\mathrm{\omega t}-\raisebox{1ex}{$\mathrm{\pi }$}\!\left/ \!\raisebox{-1ex}{$4$}\right.\right)$, the phase constant can be shown as?

Equation of motion of a particle is given by $\mathrm{a}=-\mathrm{bx}$, where $\mathrm{a}$ is the acceleration, $\mathrm{x}$ is the displacement from the mean position and $\mathrm{b}$ any constant. The time period of the particle is

If SHM is represented by $\mathrm{X}=\mathrm{A} \cos \left(\mathrm{\omega t}+\mathrm{\varphi }\right)$, then $"\mathrm{\varphi }"$ is 

If $"\mathrm{V}"$ is the magnitude of velocity $"\mathrm{A}"$ is the magnitude of displacement, then at the mean position of the particle performing SHM-

If simple harmonic motion is represented by $\mathrm{X}=\mathrm{A} \cos \left(\mathrm{\omega t}+\mathrm{\varphi }\right)$, then $\text{'}\mathrm{\omega }\text{'}$ is-

One end of a rod of length $L$ is fixed to a point on the circumference of a wheel of radius $R$. The other end is sliding freely along a straight channel passing through the centre $O$ of the wheel as shown in the figure below. The wheel is rotating with a constant angular velocity $\omega$ about $O$. Taking $T=\frac{2\pi }{\omega }$, the motion of the rod is

Match the following entries in column-I and column-II with respect to an oscillating spring-block system:

A body is performing simple harmonic motion of amplitude $\mathrm{A}$ and time period $\mathrm{T}$. The figure shows position-time graph of the body. At any time $\mathrm{t}$, acceleration of the body is $f$, then which of the following graphs is/are appropriate?

A $1 \mathrm{kg}$ block attached to a spring vibrates with a frequency of $1 \mathrm{Hz}$ on a frictionless horizontal table. Two springs identical to the original spring are attached in parallel to a$8 \mathrm{kg}$block placed on the same table. So, the frequency of vibration of the $8 \mathrm{kg}$ block is 

The type of graph between length of a simple pendulum and time period is -

The function $\mathrm{y}=\mathrm{sin\omega }\mathrm{t}-\mathrm{cos\omega }\mathrm{t}$ represents

Displacement vs time curve for a particle performing SHM is as shown in the figure.

Which of the following statement is correct?

If the frequency of human heart is $1.25 \mathrm{Hz}$, the number of times the heart beats in $1 \text{min}$ is

A body of mass $M$ and charge $q$ is connected to a spring of spring constant $k$. It is oscillating along $x$ -direction about its equilibrium position in horizontal plane, taken to be at $x=0$, with an amplitude $A$. An electric field $E$ is applied along the $x$ -direction. Which of the following statements is correct?

The potential energy of a particle of mass $0.1 \mathrm{kg}$ moving along the $x$-axis, is given by $U=5x\left(x-4\right) \mathrm{J},$ where $x$ is in metres. Choose the wrong option.

A spring has a natural length of $50 \mathrm{cm}$ and a force constant of $2.0\times {10}^3{\mathrm{Nm}}^{-1}$. A body of mass $10 \mathrm{kg}$ is suspended from it and the spring is stretched. If the body is pulled down to a length of $58 \mathrm{cm}$ and released, it executes simple harmonic motion. What is the net force on the body when it is at its lowermost position of its oscillation? (Take $g=10 {\mathrm{ms}}^{-2}$).

A particle is fastened at the end of a string and is whirled in a vertical circle with the other end of the string being fixed. The motion of the particle is,

The restoring force of SHM is maximum when particle

Assertion: The time period of the SHM of a system consisting of a mass attached to spring does not depend on whether it is hanging vertically from fixed support or lying on a horizontal table with another end of the spring fixed.

Reason: In the spring block system gravity affects only the mean position. The time period depends only on mass & spring constant.