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Question

A particle moves along y-axis according to the equation y (in cm)=3sin100πt+8sin250πt6

A
the particle performs SHM
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B
the amplitude of the particle's oscillation is 5 cm
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C
the mean position of the particle is at y=- 2 cm
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D
the particle does not perform SHM
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Solution

The correct options are
A the mean position of the particle is at y=- 2 cm
B the particle performs SHM
D the amplitude of the particle's oscillation is 5 cm
The given equation can be written as
y=3sin100πt+(44cos100πt)6
=3sin100πt+4sin(100πt+ππ/2)2
or y=5sin(100π53)2
ymax=52=3
ymin=52=7
Mean position=ymax+ymin2=2 cm
298764_219320_ans.PNG

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