Home
Class 11
PHYSICS
The displacement of a particle represent...

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

A

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

B

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

C

periodic but not simple harmonic

D

non-periodic

Text Solution

Verified by Experts

The correct Answer is:
B
The displacement of motion of particle
`y= 3 cos ((pi)/(4)- 2omega t)`
`therefore v= (d)/(dt)[3 cos ((pi)/(4)- 2omega t)]`
`= 3(-2omega) [-sin((pi)/(4)- 2omega t)]`
`therefore v = 6 omega sin ((pi)/(4)-2omega t)`
Acceleration, `a= (dv)/(dt)= (d)/(dt) [6omega sin ((pi)/(4)-2omega t)]`
`therefore a = 6omega xx (-2omega)cos ((pi)/(4)- 2omega t)`
`= -12omega^(2) cos ((pi)/(4)- 2omega t)`
`= -4omega^(2) [3cos ((pi)/(4)- 2omega t)]`
`therefore a= -4omega^(2)y" ""........"(1)`
`therefore a propto -y`
This is condition of simple harmonic motion, the motion is SHM and
`omega.= 2 omega" "[therefore " Comparing equation (1) with "a= -(omega.)^(2)y]`
`therefore (2pi)/(T.)= 2omega`
`therefore T.= (2pi)/(2omega)= (pi)/(omega)`
Doubtnut Promotions Banner Mobile Dark
|

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 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:-

A particle moves in the x-y the accoding to the equation, r = (hati + 2hatj) A cos omegat . The motion of the particle is

Knowledge Check

  • 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)`

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

    A
    Simple harmonic motion of frequency `(omega)/(pi)`
    B
    Simple harmonic motion of frequency `(3omega)/(2pi)`
    C
    Non-simple harmonic motion.
    D
    Simple harmonic motion of frequency `(omega)/(2pi)`

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

    A
    the motion is oscillatory but not SHM
    B
    the motion is SHM with amplitude `a+b`
    C
    the motion is SHM with amplitude `(a^(2)+ b^(2))`
    D
    the motion is SHM with amplitude `sqrt((a^2)+(b^2))`

    • Similar Questions

    Explore conceptually related problems

    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.

    Figure shows a sine curve, as the displacement time curve of a particle executing rectilinear motion having equation x = 45 ((pi)/(2)t) . The velocit of particle at t = (2)/(3)s is

    A particle simple harmonic motion completes 1200 oscillations per minute and passes through the mean position with a velocity 3.14 ms^(-1) . Determine displacement of the particle from its mean position. Also obtain the displacement equation of the particle if its displacement be zero at the instant t = 0 .

    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 is given by x(t) = (4t ^(2) +8) meter. The instantaneous velocity of a particle at t = 2s is

    Home
    Profile