SHMHard
Question
A particle undergoes simple harmonic motion having time period T. The time taken in 
oscillation is
oscillation is Options
A.3/8T
B.5/8T
C.5/12T
D.7/12T
Solution
3/8 oscillations can split as = 
In one fourth oscillation particle will approach at amplitude position so time taken in one fourth oscillation will be T/4 and time taken in remaining 1/8th oscillation can determine by equation
x = A cos ωt
but x =
so 
= A cosωt
⇒ cos
= cosωt so ωt = 
⇒
t = 
⇒ t = 
then total time taken will be t′ =
In one fourth oscillation particle will approach at amplitude position so time taken in one fourth oscillation will be T/4 and time taken in remaining 1/8th oscillation can determine by equation
x = A cos ωt
but x =
so = A cosωt⇒ cos
= cosωt so ωt = ⇒
t = ⇒ t = then total time taken will be t′ =
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