The displacement of a particle along the x- axis is given by x=as… - Vidyadip

MCQ

The displacement of a particle along the $x-$ axis is given by $x=asin^2$$\omega t$ . The motion of the particle corresponds to

A
simple harmonic motion of frequency $\frac{\omega }{\pi }$
B
simple harmonic motion of frequency $\frac{{3\omega }}{{2\pi }}$
✓
non simple harmonic motion
D
simple harmonic motion of frequency $\frac{\omega }{{2\pi }}$

✓

Answer

Correct option: C.

non simple harmonic motion

c
$x=a \sin ^{2} \omega t=a\left(\frac{1-\cos 2 \omega t}{2}\right)$

$\left(\because \cos 2 \theta=1-2 \sin ^{2} \theta\right) $

$= \frac{a}{2}-\frac{a \cos 2 \omega t}{2}$

$\therefore \quad$ Velocity, $v=\frac{d x}{d t}=\frac{2 \omega a \sin 2 \omega t}{2}=\omega a \sin 2 \omega t$

Acceleration, $a=\frac{d v}{d t}=2 \omega^{2} a \cos 2 \omega t$

For the given displacement $x=a \sin ^{2} \omega t,$

$a \propto-x$ is not satisfied.

Hence, the motion of the particle is non simple harmonic motion.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from 13. oscillations→13. oscillations — all question types→Physics STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

A solid sphere rolls without slipping on a rough surface and the centre of mass has a constant speed $v_0$. If the mass of the sphere is $m$ and its radius is $R$, then find the angular momentum of the sphere about the point of contact

The first overtone frequency of an open organ pipe is equal to the fundamental frequency of a closed organ pipe. If the length of the closed organ pipe is $20 \,cm$. The length of the open organ pipe is........$cm$.

A uniform chain of length $2\,m$ is kept on a table such that a length of $60\,cm$ hangs freely from the edge of the table. The total mass of the chain is $4\,kg$. What is the work done in pulling the entire chain on the table ................ $\mathrm{J}$

There is a horizontal film of soap solution. On it a thread is placed in the form of a loop. The film is pierced inside the loop and the thread becomes a circular loop of radius $R$. If the surface tension of the loop be T, then what will be the tension in the thread

A travelling wave in a stretched string is described by the equation $y = A\sin (kx - \omega t)$. The maximum particle velocity is

What is the maximum number of rectangular components into which a vector can be split in space?

On increasing the length by $0.5\, mm$ in a steel wire of length $2\, m$ and area of cross-section $2\,m{m^2}$, the force required is $[Y$ for steel$ = 2.2 \times {10^{11}}\,N/{m^2}]$

The time taken by a block of wood (initially at rest) to slide down a smooth inclined plane $9.8\, m$ long (angle of inclination is ${30^o}$) is.........$sec$

Two semicircular rings of linear mass densities $\lambda $ and $3\lambda $ and of radius $R$ each are joining to form a complete ring. The distance of the centre of the mass of complete ring from its geometrical centre is

A particle is moving in a circular path of radius $r$ under the action of a force $F$. If at an instant velocity of particle is $v$, and speed of particle is increasing, then