# Pendulum Dangling from a Spring

Pendulum Dangling from a Spring

This Demonstration models the dynamics of a pendulum suspended on a spring. The spring-pendulum system has three degrees of freedom: the length of the spring ; the angle between the spring's axis and the vertical ; and the angle between the pendulum's rod and the vertical . Follow the trace of the pendulum's bob and/or pivot as you change the parameters of the system.

r(t)

θ(t)

ϕ(t)

This can be considered a limiting case of the author's Demonstration "Spring-Cart-Pendulum System".