# Resonance in a Mechanical System

1. Apr 15, 2014

### amk1995

1. The problem statement, all variables and given/known data
A mass m is attached to one end of a massless spring with a force constant k and an unstretched length l0. The other end of the spring is free to turn about a nail driven into a frictionless, horizontal surface. The mass is made to revolve in a circle with an angular frequency of revolution ω.
Question:
Calculate the length l of the spring as a function of ω.

2. Relevant equations
F = ω2*l*m
FSpring = k*l

3. The attempt at a solution
Fspring = Fcirc
-k*l = ω2*l*m

The issue I am having is how to get L by itself, or what I am supposed to do with l0. Can someone guide me on where I should head in order to solve this problem? The issue is l cancels when I divide, unless I am supposed to use l0 in place of l
Thanks!

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2. Apr 15, 2014

### nasu

You are using "l" to designate two different things.
If "l" in the first equation is the total length of the spring (radius of the circle), then the elastic force is not correct. The force does not depend on the total length.
What is the force when the length is lo?

3. Apr 15, 2014

### amk1995

The force when length lo is just omega^2 *m*lo correct?

4. Apr 15, 2014

### nasu

No. What is the elastic force ("produced" by the spring) when the spring's length is lo?
Hint: at lo the spring is unstretched.