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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 the spring constant k.
Solution
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 = - 4 k x = mg
Where, k is the spring constant of the suspension system
Time period, `T =2pi sqrt(m/(4k))`
And `"k" = ("mg")/(4x)`
`= (3000xx10)/(4 xx 0.15) = 5000 = 5xx 10^4 "N/m"`
Spring constant, k = 5 × 104 N/m
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