For the damped oscillator of Fig. 15.20, m= 250g, k= 85N/m, and b= 70g/s
What is the period of the motion?

Explanation

To find the period of the damped oscillator, we can use the formula for the period of a damped harmonic oscillator. However, since the damping is relatively small in this case, we can approximate the motion as simple harmonic motion (SHM) and use the formula for the period of a simple harmonic oscillator.

### Step-by-Step Solution:

1. **Identify the given values:**
- Mass (m) = 250 g = 0.250 kg (convert grams to kilograms)
- Spring constant (k) = 85 N/m
- Damping coefficient (b) = 70 g/s = 0.070 kg/s (convert grams to kilograms)
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