For the damped oscillator shown in previous figure, `k= 180 Nm^(-1)` and the damping constant b is `40 gs^(-1)` .Period of oscillation is given as 0.3 s, find the mass of the block . (Assume b is much less than `sqrt(km))`.

Explanation

To find the mass of the block in the damped oscillator, we can use the relationship between the period of oscillation, the spring constant \( k \), and the mass \( m \). The formula we will use is derived from the damped oscillation equations.

### Step-by-Step Solution

1. **Identify the Given Values**:
- Spring constant \( k = 180 \, \text{N/m} \)
- Damping constant \( b = 40 \, \text{g/s} = 0.04 \, \text{kg/s} \) (convert grams to kilograms)
- Period of oscillation \( T = 0.3 \, \text{s} \)
...