Question

A mass attached to a spring is free to oscillate, with angular velocity ω, in a horizontal plane without friction or damping. It is pulled to a distance x₀ and pushed towards the centre with a velocity v₀ at time t = 0. Determine the amplitude of the resulting oscillations in terms of the parameters ω, x₀ and v₀. [Hint: Start with the equation x = a cos (ωt+θ) and note that the initial velocity is negative.]

Answer 1

The displacement equation for an oscillating mass is given by:

x =

Where,

A is the amplitude

x is the displacement

θ is the phase constant

Velocity,

At t = 0, x = x₀

x₀ = Acosθ = x₀ … (i)

And,

… (ii)

Squaring and adding equations (i) and (ii), we get:

Hence, the amplitude of the resulting oscillation is.