Home
Class 11
PHYSICS
Show that the motion of a particle repre...

Show that the motion of a particle represented by `y= sin omega t- cos omega t` is simple harmonic with a period of `(2pi)/(omega)`.

Text Solution

Verified by Experts

Displacement `y= sin omega t - cos omega t`
`therefore y= sqrt(2) [(1)/(2) sin omega t- (1)/(sqrt(2)) cos omega t]`
`therefore y= sqrt(2) [cos (pi)/(4)sin omega t - sin (pi)/(4) cos omega t]`
`therefore y= sqrt(2) sin (omega t-(pi)/(4))`
comparing this euqation with general equation of SHM `y= A sin (omega t + phi)`,
Amplitude A= 2 unit
Angular frequency, `omega = (2pi)/(T)`
`therefore T= (2pi)/(omega)`
`therefore omega = (2pi)/(T)`
`therefore T= (2pi)/(omega)`
Given function represent SHM with a periodic time `T= (2pi)/(omega)`.
Promotional Banner

Topper's Solved these Questions

  • OSCILLATIONS

    KUMAR PRAKASHAN|Exercise SECTION-D (NCERT EXEMPLAR SOLUTION LONG ANSWER QUESTIONS)|8 Videos

  • OSCILLATIONS

    KUMAR PRAKASHAN|Exercise SECTION-E (MCQs ASKED IN GUJARAT BOARD AND COMPETITIVE EXAMS)|66 Videos

  • OSCILLATIONS

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

Out of the following functions representing motion of a particle which represent SHM? (a) y= sin omega t- cos omega t (b) y= sin^(2) omega t (c ) y= 5cos ((3pi)/(4)-3 omega t) (d) y= 1+ omega t+ omega^(2) t^(2)

The displacement of a SHM particle is y= 3 sin omega t+4 cos omega t then its amplitude will be……

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

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

When two displacements represented by y_(1)= a sin(omega t)" and "y_(2)= b cos (omega t) are superimposed the motion is…….

The displacement of a particle executing simple harmonic motion is given by y= A_(0) +A sin omega t+ B cos omega t . Then the amplitude of its oscillation is given by:

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.

Which of the following functions of time represent (a) simple harmonic motion and (b) periodic but not simple harmonic? Give the period for each case. (1) sinomegat-cosomegat (2) sin^(2)omegat

Which of the following functions of time represent (a) simple harmonic, (b) periodic but not simple harmonic, and (c) non-periodic motion? Give period for each case of periodic motion ( omega is any positive constant): (a) sinomegat-cosomegat (b) sin^(3)omegat (c) 3cos(pi//4-2omegat) (d) cosomegat+cos3omegat+cos5omegat (e) exp(-omega^(2)t^(2)) (f) 1+omegat+omega^(2)t^(2)