Velocity and Acceleration in Simple Harmonic Motion

A particle executes S.H.M with amplitude$\text{'}a\text{'}$and time period $T.$ The displacement of the particle when its speed is half of maximum speed is $\frac{\sqrt{x}a}{2}.$ The value of $x$ is ____________ .

A particle performs simple harmonic motion with amplitude $A.$ Its speed is tripled at the instant that it is at a distance $\frac{2}{3}A$ from equilibrium position. The new amplitude of the motion is

If the displacement $\left(x\right)$ and velocity $\left(v\right)$ of a particle executing SHM are related through the expression $3v^2=30-x^2.$ If the time period of the particle is $T=\pi \sqrt{n}$, then what is the value of $n?$

If a simple pendulum oscillates with an amplitude of $50 \mathrm{mm}$ and time period of $2 \mathrm{s}$, then its maximum velocity is

The velocity-time diagram of a harmonic oscillator is shown in the below figure. The frequency of oscillation is

The displacement-time graph of a particle executing SHM is as shown in the figure.

The corresponding force-time graph of the particle is

The acceleration of a particle varies with displacement as $a=-4x$. At $x=4 \mathrm{m}$ and $t=0$, particle is at rest. Select the correct alternative.

The vertical motion of a huge piston in a machine is approximately simple harmonic with a frequency of $0.50 {\mathrm{s}}^{-1}$. A block of $20 \mathrm{kg}$ is placed on the piston. The maximum amplitude of the piston's simple harmonic motion, for the block and the piston to remain together is

If the maximum velocity and acceleration of a particle executing SHM are equal in magnitude, the time period will be

Particle performing $\mathrm{S}.\mathrm{H}.\mathrm{M}.$ starts from extreme position. Plot a graph of displacement, velocity and acceleration against time.

Particle performing $\mathrm{S}.\mathrm{H}.\mathrm{M}.$ starts from mean position. Plot a graph of displacement, velocity and acceleration against time.

A body describes $\mathrm{S}.\mathrm{H}.\mathrm{M}.$ in a path $0.12\mathrm{m}$ long. Its velocity at the centre of the line is $0.12\mathrm{m}/\mathrm{s}.$ Find the period, and magnitude of velocity at a distance $\sqrt{3}\times {10}^{-2}\mathrm{m}$ from the central position.

A particle executes $\mathrm{S}.\mathrm{H}.\mathrm{M}.$ with amplitude of $10\mathrm{cm}$ and period of $10\mathrm{s}.$ Find the $\left(\mathrm{i}\right)$ velocity, $\left(\mathrm{ii}\right)$ acceleration of the particle at a distance $5\mathrm{cm}$ from the equilibrium position.

A particle is executing $\mathrm{S}.\mathrm{H}.\mathrm{M}.$ of amplitude $5\mathrm{cm}$ and period of  $2\mathrm{s}.$ Find the speed of the particle at a point where its acceleration is half of its maximum value.

The acceleration, '$a$' of a particle moving in a straight line varies with displacement, $\text{'}s\text{'}$ according to relation $a\mathit{=}\mathit{2}\mathit{ }s\mathit{,}$ then velocity of the particle vary with displacement as (given that velocity is zero at zero displacement):

A highly rigid cubical block $A$ of small mass $M$ and side $L$ is fixed rigidly on to another cubical block $B$ of the same dimensions and of low modulus of rigidity $\eta$ such that the lower face of block $A$ completely covers  the upper face of block $B$. The lower face of block $B$ is rigidly held on a horizontal surface. A small force $F$ is applied perpendicular to one of the side faces of block $A$. When the force is withdrawn, block $B$ executes small oscillations, the time period is given by 

A particle executing S.H.M. has amplitude $0.01 \mathrm{m}$ and frequency $60 \mathrm{Hz}$. The maximum acceleration of the particle is

A spring having with a spring constant $1200 \mathrm{N} {\mathrm{m}}^{-1}$ is mounted on a horizontal table as shown.. A mass of $3 \mathrm{kg}$ is attached to the free and of the spring. Then the mass is pulled sideways to a distance of $2.0 \mathrm{cm}$ and released. Determine (i) maximum acceleration of the mass, and (ii) the maximum speed of the mass

A body describes simple harmonic motion with an amplitude of $5 \mathrm{cm}$ and a period of $0.2 \mathrm{s}$. The velocity of the body when the displacement is $3 \mathrm{cm}$ is $\left(N\pi \right) \mathrm{m} {\mathrm{s}}^{-1}$. Find $N$.

A body describes simple harmonic motion with an amplitude of $5 \mathrm{cm}$ and a period of $0.2 \mathrm{s}$. Find the acceleration and velocity of the body when the displacement is $5 \mathrm{cm}$.