## College Physics (4th Edition)

We can write an expression for the initial value of the energy: $E_1 = \frac{1}{2}m~A_1^2~\omega^2$ Note that $A_2 = \frac{A_1}{20.0}$. We can find the new value of the energy: $E_2 = \frac{1}{2}m~A_2^2~\omega^2$ $E_2 = \frac{1}{2}m~(\frac{A_1}{20.0})^2~\omega^2$ $E_2 = \frac{1}{400}\times \frac{1}{2}m~A_1^2~\omega^2$ $E_2 = \frac{1}{400}\times E_1$ The pendulum's energy has decreased by a factor of 400 in that time.