*Reference:** Beginning Physics I*

**CHAPTER 12****: SIMPLE HARMONIC MOTION (SHM)**

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**KEY WORD LIST**

**Simple Harmonic Motion, Periodic Motion, Period, Frequency, Reference Circle, Time Interval, SHM Time Equations, Spring Motion, Torsional Motion, Simple Pendulum**

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## GLOSSARY

For details on the following concepts, please consult **CHAPTER 12****.**

**SIMPLE HARMONIC MOTION (SHM)**

It is the back-and-forth type vibratory motion of an object that is subjected to Hooke’s Law type force, which is a restoring force that is proportional to the displacement from the equilibrium position (*F = **-k x*). Since the force is varying, the acceleration of the object, and its velocity is also varying.

The uniformity of circular motion and rotation does not *occur* in SHM.

**PERIODIC MOTION**

Periodic motion is motion repeated in equal intervals of time.

**PERIOD (T)**

The period *(T)* is defined as the time to make one complete repetition of the motion. Thus, *T* is the time interval from when the object traverses any position *x* moving in a given direction to the next time the object traverses position *x* moving in the same direction.

**FREQUENCY (f)**

The frequency

*f*of the periodic motion is the number of repetitions per second. It is the reciprocal of the period:

*f = 1/T*.

**REFERENCE CIRCLE**

Consider a particle undergoing uniform circular motion on a circle about the origin of a coordinate system.

As the particle moves around the circle, its shadow moves back and forth along the x-axis. Finding the time equations for the shadow’s motion is equivalent to finding the time equations for SHM. For this reason, this circle is called the *reference circle* for SHM.

**TIME INTERVAL**

**SHM TIME EQUATIONS**

In general,

**SPRING MOTION**

**TORSIONAL MOTION**

**SIMPLE PENDULUM**

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