The Damped Nonlinear Pendulum

​
ω
0
0.9
γ
0.3
t
15.
plot type
stream
density
θ(0) = 1.25 θ'(0) = -0.40
The plots show the motion of a harmonic oscillator with damping, in phase space on the left and as a function of time on the right, with the position of the pendulum in the top-right corner. The equation of motion is
′′
θ
(t)+γ
′
θ
(t)+
2
ω
0
sinθ(t)0
, where
ω
0
is the natural frequency and
γ
is the damping constant. This equation does not take the form of the usual approximation
sin(θ)≈θ
.
Nonlinear analogs of underdamping and overdamping can be observed.
The second-order equation can be solved by splitting it into two first-order equations.

External Links

Simple Harmonic Oscillator (ScienceWorld)
Damped Simple Harmonic Motion (Wolfram MathWorld)
Underdamped Simple Harmonic Motion (Wolfram MathWorld)
Critically Damped Simple Harmonic Motion (Wolfram MathWorld)
Overdamped Simple Harmonic Motion (Wolfram MathWorld)
Phase Space Trajectory (ScienceWorld)

Permanent Citation

Enrique Zeleny
​
​"The Damped Nonlinear Pendulum"​
​http://demonstrations.wolfram.com/TheDampedNonlinearPendulum/​
​Wolfram Demonstrations Project​
​Published: March 7, 2011