You are riding an automobile of mass 3000kg. Assuming that you are examining the oscillation characteristics of its suspension system. The suspension sags 15cm when the entire automobile is placed on it. Also, the amplitude of oscillation decreases by` 50%` during one complete oscillation. Estimate the values of (a) the spring constant k and (b) damping constant b for the spring and shock absorber system of one wheel, assuming that each wheel supports `750kg.g=10m//s^(2)`.

Explanation

To solve the problem step by step, we will first determine the spring constant \( k \) and then the damping constant \( b \).

### Step 1: Calculate the Spring Constant \( k \)

1. **Identify the given values:**
- Mass of the automobile \( M = 3000 \, \text{kg} \)
- Each wheel supports \( m = \frac{M}{4} = \frac{3000}{4} = 750 \, \text{kg} \)
- The sag of the suspension \( x = 15 \, \text{cm} = 0.15 \, \text{m} \)
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