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Two S.H.M. Y1 = A sin(wt) and y2= A cos(wt) w = omega are superimposed on a particle of mass m.The total mechanical energy of the particle is? a. 0.5m(mA)square b. m (wA)square c. 0.25 m(wA)square d. Zero

Two S.H.M. Y1 = A sin(wt) and y2= A cos(wt) w = omega are superimposed on a particle of mass m.The total mechanical energy of the particle is?

a. 0.5m(mA)square

b. m (wA)square

c. 0.25 m(wA)square

d. Zero

Grade:11

2 Answers

Khimraj
3007 Points
4 years ago
Resultant wave is given by
Y = Y1 + Y2
Y = A( sinwt + coswt)
Y = A[ sin(wt) + sin(90 + wt)]
Y = A[ 2sin((2wt + 90)/2)cos(90/2)]
Y = A[\sqrt{2}sin(wt + 45)]
Y = \sqrt{2}Asin(wt + 45)
SO total energy E = ( ½ )mw2(\sqrt{2}A)2 = m(wA)2.
Hope it clears.
If you like answer then please approve it.
Kushagra Madhukar
askIITians Faculty 629 Points
2 years ago
Dear student,
Please find the attached answer to your question below.
 
Resultant wave is given by
Y = Y1 + Y2
Y = A(sinwt + coswt)
Y = A[sin(wt) + sin(90 + wt)]
Y = A[2sin((2wt + 90)/2)cos(90/2)]
Y = A[√2sin(wt + 45)]
Y = √2Asin(wt + 45)
SO total energy E = ( ½ )mw2(√2A)2 = m(wA)2.
 
Hope it helps.
Thanks and regards,
Kushagra

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