Home
Class 12
PHYSICS
Three simple harmonic motions in the sam...

Three simple harmonic motions in the same direction having the same amplitude and same period are superposed. If each differ in phase from the next by `45^(@)`, then

A

resultant amplitude is `(1+sqrt(2))a`

B

phase of the resultant motion relative to the first is `90^(@)`

C

energy associated with the resultaing motion is `(3 + 2sqrt(2))` time the energy associated with any single motion

D

resulting motion is not simple harmonic

Text Solution

Verified by Experts

The correct Answer is:
A, C
From susperposition principal
`y = y_(1) + y_(2) + y_(3)`
`= asin omegat + a sin(omegat + 45^(@)) + asin (omegat + 90^(@))`
`= a[sin omegat + sin (omegat +90^(@))] + a sin (omegat + 45^(@))`
`= 2asin(omegat + 45^(@))cos 45^(@) + a sin (omegat + 45^(@))`
`= (sqrt(2) + 1) a sin (omegat + 45^(@)) = A sin (omegat + 45^(@))`
Therefore, resultant motion is simple harmonic of amplitude. `A = (sqrt(2) + 1)` and which differ in phase by `45^(@)` relative to the first.
`:. (E_("resultant"))/(E_("single")) = (A/a)^(2) = (sqrt(2) + 1)^(2) = (3+2sqrt(2))`
`:. E_("resultant") = (3+2sqrt(2))E_("single")`
Promotional Banner

Topper's Solved these Questions

  • SIMPLE HARMONIC MOTION

    ALLEN|Exercise Match The Column|9 Videos

  • SIMPLE HARMONIC MOTION

    ALLEN|Exercise Paragraph|3 Videos

  • SIMPLE HARMONIC MOTION

    ALLEN|Exercise Exercise-05 [B]|12 Videos

  • RACE

    ALLEN|Exercise Basic Maths (Wave Motion & Dopplers Effect) (Stationary waves & doppler effect, beats)|25 Videos

  • TEST PAPER

    ALLEN|Exercise PHYSICS|4 Videos

Similar Questions

Explore conceptually related problems

Three simle harmionic motions in the same direction having the same amplitude (a) and same period are superposed. If each differs in phase from the next by 45^@ , then.

Three simple harmonic motions in the same direction having same amplitude and the same period are superposed. If each differs in phase from the next by lambda//2 then which of the following is wron. ( i ) Resultant amplitude is (sqrt(2)+1) a ( ii ) Phase of resultant motion relative to first is 90^(@) ( iii ) The energy associated with the resulting motion is 3 times the energy associated with any single motion

Three simple harmonic motions in the same direction having each of amplitude "a" and the same period are superposed. If each differs in phase from the next by pi//4 then

Three simple harmonic motions in the same direction each of amplitude a and periodic time T , are superposed. The first and second and the second and third differ in phase from each other by (pi)/(4) , with the first and third not being identical . Then.

A particle is subjected to two simple hasrmonic motions in the same direction having equal amplitudes and equal frequency. If the resultant amplitude is equal to the amplitude of the individual motions, find the phase difference between the individual motions.

A particle is subjected to two simple harmonic motions in the same direction having equal amplitude and equal frequency. If the resultant amplitude is equal to the amplitude of individual motions, what is the phase difference between the motions.

A particle is subjected to two simple harmonic motion in the same direction having equal amplitudes and equal frequency. If the resultant amplitude is equal to the amplitude of the individual motions. Find the phase difference between the individual motions.

A particle is subjected to two simple harmonic motions in the same direction having equal amplitudes and equal frequency. If the resulting amplitude is equal to the amplitude of individual motions, the phase difference between them is

When two mutually perpendicular simple harmonic motions of same frequency, amplitude and phase are susperimposed

Three simple harmonic motion of equal amplitudes A and equal time periods in the same direction combine. The phase of the second motion is 60^(@) ahead of the first and the phase of the third motion is 60^(@) ahead of the second. Find the amplitude of the resultant motion.