damped harmonic oscillation

exponential

 last updated: 2003-07-19

Suppose a harmonic oscillation that is damped by a force, which is magnitude proportional to the velocity 1). This is called a free damped harmonic oscillation. There are three possible situations, which are treated on this page.
The following curves give the amplitude as function of time.

strong damping

h09dam1f.gif (1386 bytes)

h11dam1.gif (1864 bytes)The function is the product of an exponential function and a hyperbolic sine.


 

weak damping

h09dam2f.gif (1381 bytes)

h11dam2.gif (1941 bytes)The function is the product of an exponential function and a sine.

 

 

 

semi weak damping

h09dam3f.gif (1356 bytes)

h11dam3.gif (1835 bytes)The function is the product of an exponential function and a line.

 

 

 

 

notes

1) Differential equation: y'' + a y' + b y = 0 with y(0) = 0.

Kuipers 1966 p.345.