Free Vibrations of a Spring-Mass-Damper System

initial displacement

1

initial velocity

0

mass m

1

dampening c

0.05

spring stiffness k

1

release system

The derivation here follows the usual form given in [1], in which

m

,

c

, and

k

are the mass, damping coefficient, and spring stiffness, respectively. The variable in this system is

x(t)

. Applying Newton's second law gives the differential equation

¨

x

+2n



x

+

2

p

x=0

, where

2

p

=k/m

and

2n=c/2

.