If x, v and a denote the displacement, the velocity and the acceleration of a particle executing simple harmonic motion of time period T, then, which of the following does not change with time?
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
(a, b)
If x = a sin ( ω t + φ )
Then V = 
= a ω cos ( ω t + φ )
a = 
= – a ω 2 sin ( ω t + φ )
Time period, T = const.
= – ω 2 T = const.
a 2 T 2 + 4 π 2 v 2 =
a 2 ω 4 sin 2 ( ω t + φ ). 
+ 4 π 2 a 2 ω 2 cos 2 ( ω t + φ )= a
2 ω 2 4 π 2 [sin 2 ( ω t + φ )
+ cos 2 ( ω t + φ )]
= a 2 ω 2 4 π 2 = const.
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