Simple Harmonic Motion Part 1

Describe simple harmonic motion

An oscillation in which the acceleration is directly proportional to displacement from a fixed equilibrium position, and is always directed towards the equilibrium position

State the two (defining) conditions for an object to be performing SHM

• Acceleration is proportional to displacement

• But in the opposite direction

In SHM state the relationship between the restoring force and displacement

The restoring force acting towards equilibrium is directly proportional to the displacement from equilibrium

For SHM state the trig graph similar to displacement against time

x=Cos(t)

For SHM state the trig graph similar to velocity against time

v=-sint(t)

For SHM state the trig graph similar to acceleration against time

-cos(t)

State the shape of acceleration and velocity against displacement (a=-w²x)

Acceleration against displacement: Directly proportional in the negative

Velocity against displacement: Circle (about the origin)

$\omega$in circular motion is called angular speed, in SHM its called…because…

Angular frequency the objects oscillating

State the equations for Maximum Kinetic, elastic potential and gravitational energy in SHM

• $$E_{k\max}=\frac12m\omega^2A^2$$

• $E_{p\max}=\frac12kA^2$ ← Elastic

• $E_{p^{}\max}=mg\Delta h$ ← Gravitational