Introduction to Harmonic Motion

Simple Harmonic Motion

Damped Harmonic Oscillators

Under damped systems

Over damped systems

Critically damped systems

Equations of motion for a damped pendulum

Applet

Equations of motion for a damped pendulum

The equations from the previous sections can be applied directly to systems such as springs. They can also be applied to model the motion of a pendulum, as follows:

where g is the acceleration due to gravity, l is the length of the wire/rod the mass is attached to and α is the damping constant. The presence of the sin(θ) term makes the equation unintegrable, however. By only considering values of θ where |θ| << 1, then sin(θ) ≈ θ. The equation now becomes

which can now be calculated as in the previous sections.

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