Simple harmonic motion and damping

Lamarr · 2012-08-13T01:25:56+00:00

I have to solve the following D.E. which describes how the amplitude of oscillation r, changes with time. r=f(t) \frac{dr^{2}cos^{2}t}{dt}=rsint How do I find r?

Thread 'How does time derivative commute from one variable to another?'

I'm reviewing Meirovitch's "Methods of Analytical Dynamics," and I don't understand the commutation of the derivative from r to dr: $$ \mathbf{F} \cdot d\mathbf{r} = m \ddot{\mathbf{r}} \cdot d\mathbf{r} = m\mathbf{\dot{r}} \cdot d\mathbf{\dot{r}} $$

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Thread 'How does time derivative commute from one variable to another?'

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