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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
3 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 629 Points
one year 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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