Summary
When a spring is stretched or compressed horizontally, a force is created as
the spring tries to return to its equilibrium position. The force it exerts in
response is given by Hooke’s law: Fs = −kx.
During oscillation, the force on the block when it is at equilibrium is zero,
while the speed is at a maximum.
At amplitude, when displacement from equilibrium is largest, the force and
magnitude of acceleration are both at their maximum.
The trading off of energy between potential and kinetic causes oscillations.
Each cycle of oscillation occurs in the same amount of time.
- The amount of time it takes to complete a cycle is called a period
and is expressed in seconds per cycle.
- The number of cycles that can be completed in a unit of time is
called the frequency of the oscillations and is expressed in cycles
per second.
The forces at play in the vertical motion of a spring are very similar to those
in horizontal motion. The only difference is that, due to gravity, the vertical
motion of a spring equilibrium is not at the spring’s natural length.
For an object moving with simple harmonic motion, the period and frequency
are independent of the amplitude.
Displacement of a simple pendulum is measured by the angle that it makes
with the vertical. A pendulum’s restoring force is provided by gravity and is
proportional to the displacement.
For small angles, a pendulum exhibits simple harmonic motion.
The period and frequency of a pendulum do not depend on the mass.
