Q.

A block of mass m attached to a spring of force constant k oscillates with angular velocity ω in a horizontal plane without friction. If initially (t = 0 ), it is pulled to a distance x0 and pushed towards the centre with a velocity v0, then find the amplitude of oscillations in terms of ω, x0 and v0

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a

v02ω2−x02

b

ω2v02+x02

c

x02ω2+v02

d

v02ω2+x02

answer is D.

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Detailed Solution

let the displacement of the block at instant of time t be, x=Acos⁡(ωt+ϕ)At t = 0, x=x0∴x0=Acosϕ…(I)Velocity, ν=dxdt=−Aωsin⁡(ωt+ϕ)At t = 0, ν=−ν0∴−ν0=−Aωsin⁡ϕor Asin⁡ϕ=ν0ω. …. (ii)squaring and adding (i) and (ii), we getA2sin2⁡ϕ+cos2⁡ϕ=ν02ω2+x02A=ν02ω2+x02
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A block of mass m attached to a spring of force constant k oscillates with angular velocity ω in a horizontal plane without friction. If initially (t = 0 ), it is pulled to a distance x0 and pushed towards the centre with a velocity v0, then find the amplitude of oscillations in terms of ω, x0 and v0