Simple Harmonic Motion Overview

Introduction

We have considered the motion of objects with respect to time and characteristics of physical states with respect to displacement (with respect to space). The foundation of many extremely important physical phenomena are based on functions that vary both in time and in space. A bridge to considering such functions is to consider objects that exhibit oscillatory motion, such as springs and pendulums. Nearly all object exhibit these characteristics, and possess a unique set of frequencies at which they absorb energy from an external stimulus; not only springs and pendulums, but also musical instruments, buildings, drinking glasses, airplanes, bridges and nearly every object of interest. This characteristic frequency, the resonant frequency, is of tremendous importance to scientists and engineers. Even atoms and molecules exhibit such resonances leading to important applications and diagnostic tools. This topic is the very basis of quantum mechanics.

Essential Questions

What is periodic motion?
What is frequency?
What is period?
What is the relationship between frequency and period?
In simple harmonic motion, what is amplitude?
How is simple harmonic motion (SHM) related to uniform circular motion (UCM)?
Is the mass on the end of a spring or the extension of a mass on a spring related to the frequency of an oscillating spring?
Is the mass on a pendulum or the extension of a pendulum related to the frequency of an oscillating spring?
Is the restoring force considered to be a conservative force?
Why is resonance important?

Key Terms

amplitude - a measure of the maximum change in a periodic variable, such as displacement velocity or acceleration, from an average value over one period.
angular frequency - a scalar measure of rotation rate when considering the UCM aspects of periodic motion.
frequency - the number of occurrences of a repeating event per unit time.
oscillation - the repetitive variation in time of displacement, velocity or acceleration about a central value.
pendulum - a weight suspended from a pivot so that it can oscillate freely.
period - the interval of time within which a periodic function repeats.
resonance - the tendency of a system to oscillate with greater amplitude at some frequencies more than at other frequencies.
simple harmonic motion - a type of periodic motion where the restoring force is directly proportional to the displacement.

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