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Home » Initial volume, \( V_0 = 200 \) cm\(^3\) - Imagemakers

Initial volume, \( V_0 = 200 \) cm\(^3\) - Imagemakers

📅 April 29, 2026 👤 scraface

Apr 29, 2026

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The function is given by:
\[ V(t) = V_0 \cos^2(\omega t + \phi) \]
Using \( V(0) = \frac{V_0}{2} \):
\[ V(0) = V_0 \cos^2(\phi) = \frac{V_0}{2} \]
Divide by \( V_0 \):
\[ \cos^2(\phi) = \frac{1}{2} \quad \Rightarrow \quad \cos(\phi) = \pm...
So \( \phi = \pm \frac{\pi}{4} + k\pi \), for integer \( k \).
Using \( V\left(\frac{\pi}{2\omega}\right) = 0 \):
\[ V\left(\frac{\pi}{2\omega}\right) = V_0 \cos^2\left(\omega \cdot \f...

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