A particle moves along y-axis according to the equation y (in cm)=3sin100πt+8sin250πt−6
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+(4−4cos100πt)−6 =3sin100πt+4sin(100πt+ππ/2)−2 or y=5sin(100π−53∘)−2 ymax=5−2=3 ymin=−5−2=−7 Mean position=ymax+ymin2=−2 cm