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A particle moves on the x-axis according to the equation x = x₀ sin 2ωt. The motion is simple harmonic.

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With amplitude x_o/2

With amplitude 2x_o

With time period $\frac{π}{ω}$

With time period 2π/ω

answer is C.

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Detailed Solution

$x = {x_0}sin 2omega t$

At x = x₀,

x₀ = x₀ sin 2ωt

$Rightarrow sin 2omega t = 1$

$Rightarrow 2omega t = frac{pi }{2},left( {pi - frac{pi }{2}} right),left( {2pi + frac{pi }{2}} right),left( {3pi - frac{pi }{2}} right)....$

$therefore t = frac{pi }{{4omega }},frac{{5pi }}{{4omega }},frac{{9pi }}{{4omega }},frac{{11pi }}{{4omega }},....$

$therefore T = left( {frac{{5pi }}{{4omega }} - frac{pi }{{4omega }}} right) = left( {frac{{9pi }}{{4omega }} - frac{{5pi }}{{4omega }}} right) = left( {frac{{11pi }}{{4omega }} - frac{{9pi }}{{4omega }}} right) = ....$

$Rightarrow T = frac{pi }{omega }.$

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