# NCERT Class 11 Physics Solutions: Chapter 14 – Oscillations-Part 15

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Question 14.21:

You are riding in an automobile of mass . Assuming that you are examining the oscillation characteristics of its suspension system. The suspension sags when the entire automobile is placed on it. Also, the amplitude of oscillation decreases by during one complete oscillation. Estimate the values of

(a) The spring constant and

(b) The damping constant b for the spring and shock absorber system of one wheel, assuming that each wheel supports .

Explanation:

Mass of the automobile,

Displacement in the suspension system,

There are springs in parallel to the support of the mass of the automobile.

The equation for the restoring force for the system:

Where, k is the spring constant of the suspension system

Time period,

And,

Spring constant,

Explanation:

Each wheel supports a mass,

For damping factor , the equation for displacement is written as:

The amplitude of oscillation decreases by.

Where,

Therefore, the damping constant of the spring is .