Simple Harmonic Motion with Impulse

[conorordan]

Homework Statement

A particle P of mass 0.6kg is attached to one end of a light elastic spring of modulus of elasticity 72N and natural length 1.2m.
The other end of the spring is fixed to a point A on the smooth horizontal table on which P rests. Initially P is at rest and is 1.2m from A.
The particle receives an impulse of 3Ns in the direction AP.
Given that t seconds after the impulse the displacement of P from its initial position is x metres.

Find an equation for x in terms of t

Homework Equations

Tension in a spring, T = \frac{\lambda x}{l}

The Attempt at a Solution

I know the answer will be in the form x=asin(ωt) and I am competent with finding the period etc but it is the impulse that is throwing me off.

 

[SammyS]

Homework Statement

A particle P of mass 0.6kg is attached to one end of a light elastic spring of modulus of elasticity 72N and natural length 1.2m.
The other end of the spring is fixed to a point A on the smooth horizontal table on which P rests. Initially P is at rest and is 1.2m from A.
The particle receives an impulse of 3Ns in the direction AP.
Given that t seconds after the impulse the displacement of P from its initial position is x metres.

Find an equation for x in terms of t

Homework Equations

Tension in a spring, T = \frac{\lambda x}{l}

The Attempt at a Solution

I know the answer will be in the form x=asin(ωt) and I am competent with finding the period etc but it is the impulse that is throwing me off.

The impulse will give the mass an (almost) instant momentum.