


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. 