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
- 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)?
- Is the motion simple harmonic for any combination of values of L, k, and H?
- What is the first nonzero term in the Taylor series expansion for the force on the mass Fx
about the equilibrium point when L?
- 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).