For the damped oscillator of Fig. 15.20, m= 250g, k= 85N/m, and b= 70g/s
How long does it take for the amplitude of the damped oscillations to drop to half its initial value?

Explanation

To solve the problem of how long it takes for the amplitude of a damped oscillator to drop to half its initial value, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given values**:
- Mass \( m = 250 \, \text{g} = 0.25 \, \text{kg} \)
- Spring constant \( k = 85 \, \text{N/m} \)
- Damping coefficient \( b = 70 \, \text{g/s} = 0.07 \, \text{kg/s} \)
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