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MENTOR Note: Thread moved here from Classical Physics hence no template

I have a question set that I need to be able to answer before my exam next month, I know how to answer all of them except this one. I get the feeling I'm being an idiot.

Show that the simple harmonic motion solution of the simple pendulum in the form $$\theta (t) = A\cos ({\omega _0}t)$$ (constant A) conserves net mechanical energy E = K + U.

I have the equation for E as [tex]E = \frac{1}{2}(m{v^2} + mgl{\theta ^2})[/tex]

I want to show its derivative is equal to 0 obviously. After I substitute in [tex]\theta \left( t \right)[/tex] and differentiate, I get [tex]\frac{{dE}}{{dt}} = \frac{{{A^2}mgl{\omega _0}\sin (2{\omega _0}t)}}{2}[/tex]

Which is not 0... What am I doing wrong?

I have a question set that I need to be able to answer before my exam next month, I know how to answer all of them except this one. I get the feeling I'm being an idiot.

Show that the simple harmonic motion solution of the simple pendulum in the form $$\theta (t) = A\cos ({\omega _0}t)$$ (constant A) conserves net mechanical energy E = K + U.

I have the equation for E as [tex]E = \frac{1}{2}(m{v^2} + mgl{\theta ^2})[/tex]

I want to show its derivative is equal to 0 obviously. After I substitute in [tex]\theta \left( t \right)[/tex] and differentiate, I get [tex]\frac{{dE}}{{dt}} = \frac{{{A^2}mgl{\omega _0}\sin (2{\omega _0}t)}}{2}[/tex]

Which is not 0... What am I doing wrong?

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