A classical mechanics problem by Aman Joshi
Classical Mechanics
Level
3
A particle executes a periodic motion according to the relation x = 4 cos^2 (50t)sin(500t). Therefore, the motion can be considered to be the superposition of n independent simple harmonic motions, where n is
4
3
6
5
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1 solution
2cos(50t)[2cos50t×sin500t] =2cos50t[sin550t-sin450t] =2cos50t×sin550t-2cos50t×sin450t =sin600t-2sin500t+sin400t Which are equations of 3 SHM's So the answer is 3