AI Mentor

Check Your IQ

Free Expert Demo

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

Three simple harmonic motions in the same direction having the same amplitude a and same period are superposed. If each differs in phase from the next by 45⁰, then

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

The resultant amplitude is $large left( {1 + sqrt 2 } right)a$

The phase of the resultant motion relative to the first is 90°

The energy associated with the resulting motion is $large left( {3 + 2sqrt 2 } right)$ times the energy associated with any single motion

The resulting motion is not simple harmonic

answer is A.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

Let simple harmonic motions be represented by

$large {y_1}, = ,asin left( {omega t - frac{pi }{4}} right);,,{y_2}, = ,asin omega t,,,and$

$large {y_3} = ,asin left( {omega t + frac{pi }{4}} right)$ On superimposing,resultant SHM will be

$large y, = ,a[sin left( {omega t - frac{pi }{4}} right) + sin left( {omega t + frac{pi }{4}} right)]$

$large = ,aleft[ {2sin omega tcos frac{pi }{4} + sin omega t} right]$

$large = ,aleft[ {sqrt 2 sin omega t + sin omega t} right], = ,aleft( {1 + sqrt 2 } right)sin omega t$

Resultant amplitude = $large left( {1 + sqrt 2 } right)a$

Energy is S.H.M. (Amplitude)²

$large therefore frac{{{E_{operatorname{Re} sultan t}}}}{{{E_{operatorname{Sin} gle}}}}, = ,{left( {frac{A}{a}} right)^2} = ,{left( {sqrt 2 + 1} right)^2} = ,left( {3 + 2sqrt 2 } right)$

$large Rightarrow ,{E_{operatorname{Re} sultan t}},, = ,,(3 + 2sqrt 2 ){E_{operatorname{Sin} gle}}$

Watch 3-min video & get full concept clarity

courses

No courses found

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Online Course for IIT JEE

Best Online Course for NEET

Best Online Course for CBSE

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Get Expert Academic Guidance – Connect with a Counselor Today!