- #1

SaraM

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__1. Homework Statement__A particle of mass m is attached to the end of a light spring of equilibrium length a, whose other end is fixed, so that the spring is free to rotate in a horizontal plane. The tension in the spring is k times its extension. Initially the system is at rest and the particle is given an impulse that starts its movement at right angles to the spring with velocity v. Write down the equations of motion in polar co-ordinates.

__2. Homework Equations__Radial Force F

_{r}= -k⋅r

Radial acceleration a

_{r}= mv

^{2}/r

Tangential Force F

_{θ}= Torque = r⋅F

__3. The Attempt at a Solution__I tried applying Newton's second law for both the radial and tangential components.

In r : ma

_{r}= -k⋅r ⇒ r = a⋅cos(ωt) (which is not the correct answer)

In θ: 1- mr⋅a

_{θ}= r⋅F (got me nowhere)

2- v

_{θ}= v/r=ω ; ω=√k/m (how do I recover θ(t) from it?)

Thank you in advance