Answer
In ten cycles, the energy decreases by 9.75%
Work Step by Step
We can write an expression for the initial value of energy:
$E_1 = \frac{1}{2}m~A_1^2~\omega^2$
Note that $A_2 = 0.950~A_1$. We can find the new energy of the pendulum:
$E_2 = \frac{1}{2}m~A_2^2~\omega^2$
$E_2 = \frac{1}{2}m~(0.950~A_1)^2~\omega^2$
$E_2 = 0.9025\times \frac{1}{2}m~A_1^2~\omega^2$
$E_2 = 0.9025\times E_1$
We can find the percentage decrease in the energy:
100% - 90.25% = 9.75%
In ten cycles, the energy decreases by 9.75%.
