SHMHard
Question
Which of the following functions represent SHM?
Options
A.sin 2ωt
B.sin 2ωt
C.sin ωt + 2 cos ωt
D.sin ωt + cos 2ωt
Solution
Equation of S.H.M x − x0 = a sin (ωt + φ) ⇒ x = x0 + a sin (ωt + φ)
(A) x = sin2ωt
(B) x = sin2 ωt =
⇒ x −
cos2 ωt
(C) x = sin ωt + 2cos ωt = sin (ωt + φ) {φ = tan-1 2}
So represent equation of S.H.M
(D) But sin ωt + cos2 ωt cannot write as sin (ωt + φ)
sin ωt + cos2 ωt sin (ωt + φ)
So it is not S.H.M equation
(A) x = sin2ωt
(B) x = sin2 ωt =
⇒ x −
cos2 ωt(C) x = sin ωt + 2cos ωt = sin (ωt + φ) {φ = tan-1 2}
So represent equation of S.H.M
(D) But sin ωt + cos2 ωt cannot write as sin (ωt + φ)
sin ωt + cos2 ωt sin (ωt + φ)
So it is not S.H.M equation
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