Question

The mechanical energy of a damped oscillator becomes half of its initial energy in 4 seconds. In another \( t \) seconds its mechanical energy becomes 12.5\% of its initial mechanical energy. Then \( t = \):

• A. 4 s
• B. 8 s
• C. 12 s
• D. 16 s

Hint:

In damped oscillations, the energy decreases exponentially over time. Use the formula \( E(t) = E_0 e^{-\gamma t} \) to relate time and energy decay.

Answer 1

The Correct Option is B

The decay of mechanical energy in a damped oscillator follows an exponential function. Using the relationship between the time and the percentage of energy decay, we calculate that the time required for the energy to drop to 12.5\% of its initial value is 8 seconds. Thus, the correct answer is option (2).