Pendulum Dangling from a Spring

animation

speed

fast

medium

slow

pendulum parameters

length of rod:

L

3

mass of bob:

M

1

starting angle:

ϕ

0

30°

starting speed:

ϕ

00

-0.1

spring parameters

spring constant:

k

100

mass of spring:

m

1

starting angle:

θ

0

90°

trace pivot

trace bob

resonant frequencies:

pendulum = 0.29

spring = 1.13

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

r(t)

; the angle between the spring's axis and the vertical

θ(t)

; and the angle between the pendulum's rod and the vertical

ϕ(t)

. Follow the trace of the pendulum's bob and/or pivot as you change the parameters of the system.

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