Physical pendulum period
T = period
I = moment of inertia
m = mass, g = acceleration of gravity
h = distance from pivot to center of
mass
What is the period of the
swinging meter stick?
I = 1/3 × mass × length^2
14.13 - Damped oscillations
We have considered many types of oscillations, and up until now assumed the periodic motion continued without change. But most real-world
oscillations are damped, which means they are subject to forces like friction that cause the amplitude of the motion to decrease over time.
Mountain bike shock absorbers provide an excellent demonstration of damped oscillations. A shock absorber often combines a spring with a
sealed container of fluid. Shock absorbers lessen the jolts of a bumpy trail.
To explain this in more detail, let’s consider what happens when a bike equipped with such a shock absorber hits a bump. The force from the
bump compresses the spring, with the result that less of the force from the bump passes to the rest of the bike (and the rider).
The spring then supplies a restoring force. In the absence of any other force, the rider and bike would in principle then move forever in simple
harmonic motion. However, inside a shock absorber, the spring moves a piston in a sealed cylinder of fluid. The fluid supplies what is called a
damping force.
In Concepts 1 and 2, you see a diagram of this system. The fluid (typically oil) provides a force that opposes the motion of the piston. The