Home
Class 11
PHYSICS
Two simple harmonic motions are represen...

Two simple harmonic motions are represented by `y_(1) = 10 sin"" (pi)/(4) (12t+1)" and " y_(2) = 5(sin"" 3pi t+ sqrt(3) cos 3pi t)`. Find out the ratio of their amplitudes. What are the time period of two motions.

Text Solution

Verified by Experts

`y_(1) = 10sin (pi)/(4) (12t+ 1)`
Comparing `y_(1) = 10sin (3pi t+ (pi)/(4))` with `y= A_(1) sin (omega_(1) t+phi)`
Amplitude `A_(1) = 10 cm " and "omega =3pi rads^(-1)`
`T = (2pi)/(omega) = (2pi)/(3pi) = (2)/(3)s`
and `y_(2) = 5 (sin 3pi t + sqrt(3) cos 3 pi t)`
`= 5xx2 [(1)/(2) sin 3pi t + sqrt((3)/(2)) (cos 3 pi t)]`
`y_(2) = 2xx 5[cos phi sin 3 pi t +sin phi (cos 3pi t)]`
Comparing `Y_(2) = 10 [sin (3pi + phi)]` with `y= A_(2) sin (omega_(2) t +phi)`
Amplitude `A_(2) = 10 cm" and "omega_(2) 3pi rads^(-1)`
`therefore T_(2) = (2pi)/(omega_2) = (2pi)/(3pi) = (2)/(3)" second "`
Ratio of amplitudes `(A_1)/(A_2) = (10)/(10)= 1`
and `T_(1) = T_(2) = (2)/(3)" second "`.
Promotional Banner

Topper's Solved these Questions

  • OSCILLATIONS

    KUMAR PRAKASHAN|Exercise SECTION-C (OBJECTIVE QUESTIONS)|60 Videos

  • OSCILLATIONS

    KUMAR PRAKASHAN|Exercise SECTION-C (OBJECTIVE QUESTIONS TRUE OR FALSE)|8 Videos

  • OSCILLATIONS

    KUMAR PRAKASHAN|Exercise SECTION-B (ADDITIONAL EXERCISE)|9 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

If two S.H.M.'s are represented by equation y_(1) = 10 "sin" [3pit+(pi)/(4)] and y_(2) = 5[sin(3pit)+sqrt(3)cos(3pit)] then find the ratio of their amplitudes and phase difference in between them.

Two simple harmonic motion are represented by the equation y_(1)= 0.1 sin(100 pi t+(pi)/(3)) and y_(2)= 0.1 cos pi t . The phase difference of the velocity of particle-1 with respect to the velocity of particle-2 is…………

If two waves represented by y_(1)=4sinomegat and y_(2)=3sin(omegat+(pi)/(3)) interfere at a point find out the amplitude of the resulting wave

Two simple harmonic are represented by the equation y_(1)=0.1 sin (100pi+(pi)/3) and y_(2)=0.1 cos pit . The phase difference of the velocity of particle 1 with respect to the velocity of particle 2 is.

The phase difference between two SHM y_(1) = 10 sin (10 pi t + (pi)/(3)) and y_(2) = 12 sin (8 pi t + (pi)/(4)) to t = 0.5s is

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

Two SHM are represcnted by equations y_(1)=6cos(6pit+(pi)/(6)),y_(2)=3(sqrt(3)sin3pit+cos3pit)

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.

Two waves travelling in a medium in the x-direction are represented by y_(1) = A sin (alpha t - beta x) and y_(2) = A cos (beta x + alpha t - (pi)/(4)) , where y_(1) and y_(2) are the displacements of the particles of the medium t is time and alpha and beta constants. The two have different :-

A particle of mass 50 g participates in two simple harmonic oscillations simultaneously as given by x_(1) = 10 (cm) cos [80 pi(s^(-1))t] and x_(2) = 5(cm) sin [(80 pi(s^(-1))t + pi//6] . The amplitude of particle's oscillations is given by 'A'. Find the value of A^(2) (in cm^(2)) .