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


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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The 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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Wave Displacement: Definition & Formula


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