The equation of motion for a damped linear pendulum is
where Ï?=sqrt(l/g) and ? are positive constants, with l the length of the pendulum and g gravity. If l=1, g=9.81 and ?=1/4 and ?(0)=3, how long does it take the pendulum swinging from rest to reach the position ?=0. How long does it take to reach ?=0 a second time?
The equation of motion for a damped linear pendulum is depicted.
Damped pendulum equation
For the damped pendulum equation: x"+cx'+kx=0 assume k = 9.
(a) Write down a solution to the equation. When does the solution type change as c varies?
(b) Classify the equilibrium at the origin as a "sink", "source", "spiral sink", "spiral source", "center", or "saddle".