# Tethered Mass and Spring

A mass constrained to move in the x-direction by a horizontal rod is connected to a spring of natural length L = 10. One end of the spring is connected to a movable (dragable) ceiling and the other end is connected to the mass. You can also drag the mass along the rod. You can control the height of the ceiling H which changes the stretch of the spring, the spring constant k and the natural length of the spring L.

## Questions

1. The natural length of the spring is changed from L=10 to L=5. What values of k and H will produce exactly the same position graph x(t)?
2. Is the motion simple harmonic for any combination of values of L, k, and H?
3. What is the first nonzero term in the Taylor series expansion for the force on the mass Fx about the equilibrium point when L?
4. What is the first nonzero term in the Taylor series expansion for the force on the mass Fx about the equilibrium point when L=2

## Topics

- Lagrangian mechancis
- nonlinear oscillators

## Reference

Pirooz Mohazzabi "Theory and example of intrinsically nonlinear oscillators." Am. J. of Phys., 72, 492-498 (2004).