# Resonance in a Mechanical System

## Homework Statement

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.

F = ω2*l*m
FSpring = k*l

## 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!

#### Attachments

• YF-13-44.jpg
10 KB · Views: 481

nasu
Gold Member
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?

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

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