Answer
When the pendulum swings with an amplitude of $3.0~cm$, the mechanical energy is $11.25~mJ$
Work Step by Step
We can write an expression for the initial value of mechanical energy:
$E_1 = \frac{1}{2}m~A_1^2~\omega^2$
Note that $A_2 = 1.5~A_1$. We can find the mechanical energy when the pendulum swings with an amplitude of $3.0~cm$:
$E_2 = \frac{1}{2}m~A_2^2~\omega^2$
$E_2 = \frac{1}{2}m~(1.5~A_1)^2~\omega^2$
$E_2 = 2.25\times \frac{1}{2}m~A_1^2~\omega^2$
$E_2 = 2.25\times E_1$
$E_2 = (2.25)(5.0~mJ)$
$E_2 = 11.25~mJ$
When the pendulum swings with an amplitude of $3.0~cm$, the mechanical energy is $11.25~mJ$.
