In a damped oscillation amplitude at (t = 0) is `A_(0)` and at (t = T) its value `A_(0)//2` if E (t = 0) `= E_(0)` find E (t = 2T)

Explanation

To solve the problem of finding the energy at \( t = 2T \) in a damped oscillation where the amplitude at \( t = 0 \) is \( A_0 \) and at \( t = T \) is \( \frac{A_0}{2} \), we can follow these steps:

### Step 1: Understand the relationship between amplitude and time
In damped oscillations, the amplitude \( A(t) \) at any time \( t \) can be expressed as:
\[ A(t) = A_0 e^{-bt} \]
where \( b \) is the damping coefficient.
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