Home
Class 11
PHYSICS
The displacement of a particle is repres...

The displacement of a particle is represented by the equation `y= sin^(3) omega t`. The motion is………..

A

non-periodic

B

periodic but not simple harmonic

C

simple harmonic with period `(2pi)/(omega)`

D

simple harmonic with period `(pi)/(omega)`

Text Solution

Verified by Experts

The correct Answer is:
B
Displacement of particle `y= sin^(3) omega t`
`= (3sin omega t-4sin 3 omega t)/(4)" "[therefore sin 3theta= 3sin theta- 4sin^(3)theta]`
`therefore v= (dy)/(dt)= (d)/(dt)[(3sin omega t-4sin 3omega t)/(4)]`
`therefore 4v= 3omega cos omega t -4xx3 omega cos 3 omega t`
`therefore 4v= 3omega cos omega t- 12omega cos 3 omega t`
`therefore 4(dv)/(dt)= (d)/(dt) [3omega cos omega t- 12omega cos 3omega t]`
`therefore 4a= -3omega^(2)sin omega t+ 36 omega^(2)sin 3 omega t`
`therefore a= -(3omega^(2)sin omega t- 36 omega^(2)sin 3 omega t)/(4)`
`= -omega^(2) ((3sin omega t+ 36 sin 3 omega t))/(4)`
`therefore " It is not " a propto -omega^(2)y`
Hence, motion is not SHM.
As the expression is involving sine function, hence it will be periodic.
Promotional Banner

Topper's Solved these Questions

  • OSCILLATIONS

    KUMAR PRAKASHAN|Exercise SECTION-D (NCERT EXEMPLAR SOLUTION MCQs MORE THAN ONE OPTIONS)|8 Videos

  • OSCILLATIONS

    KUMAR PRAKASHAN|Exercise SECTION-D (NCERT EXEMPLAR SOLUTION VERY SHORT ANSWER QUESTIONS)|10 Videos

  • OSCILLATIONS

    KUMAR PRAKASHAN|Exercise SECTION-C (OBJECTIVE QUESTIONS ASSERTION OR REASION)|7 Videos

  • OBJECTIVE QUESTIONS AS PER NEW PAPER STYLE

    KUMAR PRAKASHAN|Exercise CHAPTER - 8 (Match Type questions)|5 Videos

  • PHYSICAL WORLD

    KUMAR PRAKASHAN|Exercise SECTION-E (QUESTIONS FROM MODULE)|9 Videos

Similar Questions

Explore conceptually related problems

The displacement of a particle represented by the equation y= 3 cos((pi)/(4)-2 omega t) . The motion of the particle is

The displacment of a particle is represented by the following equation : s=3t^(3)+7t^(2)+4t+8 where s is in metre and t in second. The acceleration of the particle at t=1:-

The displacement of particle along the X-axis is given by x= a sin^(2) omega t . The motion of the particle corresponds to………..

The displacement of a particle varies with time according to the relation y= a sin omega t+b cos omega t ……………

The displacement of an elastic wave is given by the function y = 3 sin omega t + 4 cos omega t. where y is in cm and t is in second. Calculate the resultant amplitude.

The displacement of a progressive wave is represented by y= A sin (omegat-kx) where x is distance and t is time. Write the dimensional formula of (i) w and (ii) k.

A simple harmonic motion of a particle is represented by an equation x= 5 sin(4t -(pi)/(6)) , where x is its displacement. If its displacement is 3 unit then find its velocity.

The displacement of a particle varies with time as x = 12 sin omega t - 16 sin^(3) omega t (in cm) it is motion is S.H.M. then its maximum acceleration is

What type of motion is represented by equation Delta s= v Delta t ?

A simple harmonic motion of a particle is represented by an equation x= 0.01 sin [100 pi (t +0.05)] . Where x is metre and t is in second respectively. The value of time period is…………