A particle moves on the X-axis according to the equation x=x_o sin^2 ωt. The motion is simple harmonic
A particle moves on the X-axis according to the equation x=xo sin2 ωt. The motion is simple harmonic
(a) with amplitude xo
(b) with amplitude 2x0
(c) with time period 2π/ω
(d) with time period π/ω
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(d) with time period π/ω.
EXPLANATION:
x = x₀sin²⍵t =x₀(1-cos2⍵t)/2 →x = x₀/2 - ½x₀.cos2⍵t.
It gives the amplitude as x₀/2, hence (a) and (b) are not true. The time period is given as T=2π/(2⍵) =π/⍵. So (d) is true not (c).
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