# Simple Harmonic Motion...2

Discussion in 'Geometry and Trigonometry' started by nycmathguy, Mar 2, 2022.

1. ### nycmathguy

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Definitions and terms. Let me know if my notes are correct as stated.

Simple Harmonic Motion = SHM in short.

Simple Harmonic Motion is vibratory motion that does not lessen with time. In other words, motion without end. This is very different from Damped Harmonic Motion. In DHM, motion begins and slowly comes to an end.

SHM can be modeled using two trig functions:

1. Sine

2. Cosine

Displacement = distance between the function's resting position and location over time. In other words, displacement from rest.

| a | = amplitude

T = 2pi/w ==>period, where w = omega

f = frequency = w/2pi

Notice that f is the reciprocal of T. Can we say they are reciprocals of each other? You say?

What is frequency?

Frequency is the number of oscillations per time intervals.

NOTE:

1. IF THE FUNCTION STARTS TO MOVE AT A POSITION AWAY FROM REST, USE THE COSINE MODEL d = a cos(wt) to build your function.

2. IF THE FUNCTION STARTS TO MOVE AT THE REST POSITION, USE THE SINE MODEL
d = a sin(wt) to build your function.

You say?

nycmathguy, Mar 2, 2022