# Simple Harmonic Motion

Calpalned

## Homework Statement

My textbook states that for simple harmonic motion, the sinusoidal graph of the x (displacement) as a function of time can be created using the "Equation of motion".

## Homework Equations

The equation of motion ##A \cos (\omega t + \phi)##

## The Attempt at a Solution

I know that ##A## stretches the cosine graph vertically, but that the frequency is unaffected. How do ##\omega## and ##\phi## affect the graph?

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## Homework Statement

My textbook states that for simple harmonic motion, the sinusoidal graph of the x (displacement) as a function of time can be created using the "Equation of motion".

## Homework Equations

The equation of motion ##A \cos (\omega t + \phi)##

## The Attempt at a Solution

I know that ##A## stretches the cosine graph vertically, but that the frequency is unaffected. How do ##\omega## and ##\phi## affect the graph?
Try some values and see.

or ...

What do you know about shifting and stretching/shrinking of graphs in general?

What is the period of y = cos(x) ?

How does the graph of y = f(x + k) compare with the graph of y = f(x) ?

etc.

• Calpalned
Calpalned
Try some values and see.

or ...

What do you know about shifting and stretching/shrinking of graphs in general?

What is the period of y = cos(x) ?

How does the graph of y = f(x + k) compare with the graph of y = f(x) ?

etc.
Thank you so much! Is my understanding below valid?

##A## stretches/compresses the graph vertically
##\omega## affects the period. The larger ##\omega## is, the shorter the period.
##\phi## is the horizontal shift and it is negative. That is, a positive value of ##\phi## will shift the graph to the left.

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