Simple+Harmonic+Motion

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Simple Harmonic Motion involves the behavior of repetitive motions such as those of a pendulum or an oscillating spring.

__Basic Relationships__

Period vs. Frequency

T = (1/F)

Period is the time it takes for one complete cycle, where Frequency is the number of oscillations per unit of time.

__Pendulum Motion__

We can see here that the mass of the pendulum has no effect on its motion.

You can also use energy conservation to find the energies and velocities of the pendulum, using the initial vertical height as h in PE = mgh.

Maximum speed/KE/Tension and minimum PE will occur at the bottom of the pendulum's arc.

__Spring Motion__

Simulation and complex analysis can be found here: http://www.myphysicslab.com/spring1.html

Hooke's Law This shows the relation of the spring constant (k) and the compression of the spring (x) to the force (F) that the spring will exert.

Harmonic Motion of a weighted spring.

T is the period of this apparatus, m is the mass of the bob and k is the spring constant.