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A particle moves on the x axis according to the equation x=x 0 sin 2 (wt). The motion is simple harmonic (1) with amplitude x 0 (2) with amplitude 2x 0 (3) with time period 2pi/w (4) with time period pi/w Please help

A particle moves on the x axis according to the equation x=x0sin2(wt). The motion is simple harmonic
(1) with amplitude x0
(2) with amplitude 2x0
(3) with time period 2pi/w
(4) with time period pi/w
 
Please help

Grade:12

2 Answers

Khimraj
3007 Points
6 years ago
x = xosin2(wt)
x = xo(1 – cos2wt)/2
So x = xo/2 – (½)xocos(2wt)
SO its amplityde is xo/2
and 2w = 2pi/T
So T = pi/w.
So correct option is (4).
Hopeit clears. If you like anser then please approve it.
Kushagra Madhukar
askIITians Faculty 628 Points
3 years ago
Dear student,
Please find the answer to your question.
 
x = xosin2(wt)
x = xo(1 – cos2wt)/2
So x = xo/2 – (½)xocos(2wt)
Hence its amplitude is xo/2
and 2w = 2pi/T
=> T = pi/w.
Hence, correct option is (4).
 
Thanks and regards,
Kushagra

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