A circular disc of moment of inertia `I_(t)` is rotating in a horizontal plane about its symmetry axis with a constant angular velocity `omega_(i)`. Another disc of moment of inertia `I_(b)` is dropped co-axially onto the rotating disc. Initially, the second disc has zero angular speed. Eventually, both the discs rotate with a constant angular speed `omega_(f)`. Calculate the energy lost by the initially rotating disc due to friction.

Explanation

To solve the problem, we need to calculate the energy lost by the initially rotating disc due to friction when a second disc is dropped onto it. We will use the principle of conservation of angular momentum and the formula for kinetic energy.

### Step-by-Step Solution:

1. **Identify the Initial Conditions**:
- The first disc has a moment of inertia \( I_t \) and an initial angular velocity \( \omega_i \).
- The second disc has a moment of inertia \( I_b \) and an initial angular velocity of 0 (it is dropped onto the first disc).

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