The Damped Nonlinear Pendulum
The Damped Nonlinear Pendulum
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 (t)+γ(t)+sinθ(t)0, where is the natural frequency and is the damping constant. This equation does not take the form of the usual approximation .
′′
θ
′
θ
2
ω
0
ω
0
γ
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
External Links
Permanent Citation
Permanent Citation
Enrique Zeleny
"The Damped Nonlinear Pendulum"
http://demonstrations.wolfram.com/TheDampedNonlinearPendulum/
Wolfram Demonstrations Project
Published: March 7, 2011