The mechanical energy ( E ) of a damped oscillator is proportional to the square of its amplitude ( A ). When the amplitude becomes half of its initial valuc, the mechanical energy decrease to a quarter of its initial value. This is because the mechanical energy is given by E∝A2 So, if the initial energy is E0 and the initial amplitude is A0. When the amplitude becomes
A0
2
. E=E0(
A0
2
A0
)2=E0(
1
2
)2=
E0
4
∴ Decrease in mechanical energy of oscillator =E0−
