Question

You are riding in an automobile of mass 3000 kg. Assuming that you are examining the oscillation characteristics of its suspension system. The suspension sags 15 cm 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 lc
(b) the damping constant b for the spring and shock absorber system of one wheel, assuming that each wheel supports 75() kg.

Answer 1

Mass of the automobile, m = 3000 kg

Displacement in the suspension system, x = 15 cm = 0.15 m
There are 4 springs in parallel to the support of the mass of the automobile.
The equation for the restoring force for the system:
F = –4kx = mg
Where, k is the spring constant of the suspension system
Time period, T = 2π √m/4k
and k = mg/4x = 3000 × 10/ 4 × 0.15 = 5000 = 5 × 104 Nm
Spring Constant, k = 5 × 104 Nm

Answer 2

Hey mate ^_^

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Answer:
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(a)

m = 3000 kg
x = 0.15 m

The equation for the restoring force for the system:
F = –4kx = mg

Time period, 

T = 2π √m/4k

k = mg/4x
= 3000 × 10/ 4 × 0.15
= 5000
= 5 × 10^4 Nm

Spring Constant, k = 5 × 10^4 Nm

(b) Check this attachment

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