Aaron Boyd's Assignment 8: Difference between revisions

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\theta(t) = \theta_0cosh(t\sqrt(\frac{g}{L}))\\
\theta(t) = \theta_0cos(t\sqrt(\frac{g}{L}))\\
\end{align}
\end{align}
</math>
</math>

Latest revision as of 11:16, 19 November 2010

I decided to use laplace transforms to solve a pendulum equation. A pendulum with a weight of mass m and a massless rod length L is released from an initial angle . Find a function to determine the angle at any time t. The summation of forces yields


Polar coordinates may be easier to use, lets try that.



canceling the common mass term and rearranging a bit we get.


You can solve for the same thing from the cartesian coordinates. Taking:



you can arrive at the same answer