# Use the equations for a vertical oscillator in SHM, y = A s i n ( ? t + ? ) a n d y = ? A c o s...

## Question:

Use the equations for a vertical oscillator in SHM, {eq}y=Asin(\omega t +\phi) and y=\omega Acos(\omega t +\theta) {/eq} to derive an equation for amplitude, A, and an equation for phase angle, {eq}\phi {/eq} , as a function of initial position, {eq}y_0 {/eq} , and initial velocity, {eq}v_0 {/eq}.

## Displacement and Velocity:

A displacement during an object's motion is obtained by the velocity multiplied by the elapsed time. The velocity is a derivative of the displacement with respect to the time. Both of them are vector quantities.

## Answer and Explanation: 1

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View this answerThe given equations are

{eq}y=A \sin(\omega t +\phi)\\ dy=\omega A\cos(\omega t +\phi) {/eq}

Please note, *dy* is the time-derivative of *y*.

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Chapter 16 / Lesson 4Wave displacement refers to the relative change in position of a wave as it traveled through a medium. Learn more about the definition and formula of wave displacement and how to distinguish between distance and displacement.

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