SHMHard
Question
Function x = A sin2 ωt + B cos2 ωt + C sin ωt cos ωt represents SHM
Options
A.for any value of A, B and C (except C = 0)
B.if A = - B; C = 2B, amplitude = |B√2|
C.if A = B; C = 0
D.if A = B; C = 2B, amplitude = |B|
Solution
x = 
(1 - cos 2ωt) + 
(1 + cos 2ωt) + 
sin 2ωt
For A = 0, B = 0
x = sin 2ωt
For A = -B and C = 2B
x = B cos 2ωt + B sin 2ωt
Amplitude = |B√2|
For A = B; C = 0
x = A,
Hence this is not correct option
For A = B, C = 2B
x = B + B sin 2ωt
It is also represents SHM.
(1 - cos 2ωt) + (1 + cos 2ωt) + sin 2ωtFor A = 0, B = 0
x =
sin 2ωtFor A = -B and C = 2B
x = B cos 2ωt + B sin 2ωt
Amplitude = |B√2|
For A = B; C = 0
x = A,
Hence this is not correct option
For A = B, C = 2B
x = B + B sin 2ωt
It is also represents SHM.
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