TS EAMCET 9 May 2024 Shift 1 Solved Paper

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−‌

E0

4

=‌

3E0

4

∴ \% decrease in mechanical energy
=‌

‌ 3E0 4

E0

×100=75%