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want2graduate

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## Homework Statement

Two identical pendulums of the same mass

*m*are connected by a light spring. The displacements of the two masses are given, respectively, by x

_{a}= Acos( (w2-w1)t/2 )cos( (w2 + w1)t/2 ), x

_{b}= Asin( (w2-w1)t/2 )sin( (w2 + w1)t/2 ).

Assume that the sprint is sufficiently weak that its potential energy can be neglected and that the energy of each pendulum can be considered to be constant over a cycle of its oscillation.

Show that the energies of the two masses are are:

E

_{a}= 1/2 m * A^2 ( (w2 + w1)/2 )^2 cos^2( (w2 - w1)t/2 )

E

_{b}= 1/2 m * A^2 ( (w2 + w1)/2 )^2 sin^2( (w2 - w1)t/2 )

## Homework Equations

Energy of simple harmonic oscillator = (1/2)mw^2 (amplitude)^2

## The Attempt at a Solution

In the book's solution, it says that amplitude = A cos[ (w2 - w1)t/ 2] or A sin[ (w2 - w1)t/2 ]. Where does it get this from? What happened to the other cosine/sine term? Why is it using this particular term?

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