Is the Motion of Particle P Simple Harmonic?

AI Thread Summary
The discussion revolves around determining whether the motion of a particle P, attached to a spring, is simple harmonic after receiving an impulse. Participants suggest using Newton's second law or the Euler-Lagrange equation to set up the equation of motion. The impulse of 0.5 Ns leads to a calculation of the initial velocity of the particle. Once the initial conditions are established, the equation of motion can be derived. The thread concludes with the original poster successfully finding the answer.
mr bob
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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
 
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How about setting up the equation of motion (Newton's 2nd law F=ma, or the Euler-Lagrange equation) and solve?
 
How would i do this, impulse is applied. Would it be:-0

0.5 = 0.2v, where v is velocity?
 
mr bob said:
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.
 
Thank you both so much!
I finally got the answer.
 

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