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Thursday, November 8, 2012

Double pendulum

In case of a double pendulum find the expression for the kinetic energy of the system
We take a simple case where lengths and masses are same.see below in the figure

Here on being displaced the co-ordinates of two pendulums are
\(\begin{array}{l}{x_1} = l\sin {\theta _1}\\{y_1} = l\cos {\theta _1}\end{array}\)
For the first pendulum where \({\theta _1}\) is the angle through which the first pendulum have been displaced.
For second pendulum
\(\begin{array}{l}{x_2} = l\sin {\theta _1} + l\sin {\theta _2}\\{y_2} = l\cos {\theta _1} + l\cos {\theta _2}\end{array}\)
Where \({\theta _2}\) is the angle through which second pendulum has been displaced.
The total kinetic energy of the system is given by the expression
\(T = \frac{1}{2}m(\dot x_1^2 + \dot y_1^2) + \frac{1}{2}m(\dot x_2^2 + \dot y_2^2)\)


Which is the required result

1 comment:

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