Is the Motion of Particle P Simple Harmonic?

[mr bob]

A particle P of mass 0.2kg is attatched by an elastic spring of modulus 15N and natural length 1m to a point A of the smooth horizontal surface on which P rests. P receives an impulse of magnitude 0.5Ns in the direction AP. Show that while the string is taught, the motion of P is simple harmonic and calculate the period and amplitude of the motion.

I don't know how to even begin this one,
Any help is really appreciated.

Rob

 

[da_willem]

How about setting up the equation of motion (Newton's 2nd law F=ma, or the Euler-Lagrange equation) and solve?

 

[mr bob]

How would i do this, impulse is applied. Would it be:-0

0.5 = 0.2v, where v is velocity?

 

[Libertine]

How would i do this, impulse is applied. Would it be:-0

0.5 = 0.2v, where v is velocity?

Yes. So then you have its velocity in the centre of motion, when t=0 and can hence derive equation of motion.

 

[mr bob]

Thank you both so much!
I finally got the answer.