Theo bài: \(T_2=\dfrac{1}{3}T_1;A_2=\dfrac{1}{2}A_1\)
Năng lượng vật lúc đầu: \(E_1=\dfrac{1}{2}m\omega_1^2A_1^2=\dfrac{1}{2}m\cdot\left(\dfrac{2\pi}{T_1}\right)^2\cdot A^2_1\)
Năng lượng vật lúc sau:
\(E_2=\dfrac{1}{2}m\omega_2^2A^2_2=\dfrac{1}{2}m\cdot\left(\dfrac{2\pi}{T_2}\right)^2\cdot A_2^2=\dfrac{1}{2}m\cdot\left(\dfrac{2\pi}{\dfrac{1}{3}T_1}\right)^2\cdot\left(\dfrac{1}{2}A_1\right)^2\)
\(\Rightarrow E_2=\dfrac{1}{2}m\cdot3^2\cdot\left(\dfrac{2\pi}{T_1}\right)^2\cdot\left(\dfrac{1}{2}\right)^2\cdot A_1^2=9\cdot\dfrac{1}{4}\cdot\dfrac{1}{2}m\cdot\left(\dfrac{2\pi}{T_1}\right)^2\cdot A_1^2=\dfrac{9}{4}E_1\)
Vậy \(\dfrac{E_2}{E_1}=\dfrac{9}{4}\)
