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question mark

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

Kavan , 7 Years ago
Grade 11
anser 2 Answers
Khimraj

Last Activity: 7 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.
Approved
Kushagra Madhukar

Last Activity: 5 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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