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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.

Text Solution

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Mass M = 3000 kg
Displacement `x= 15 cm = 0.15 cm, g= 10 ms^(-2)`
There are four spring systems. If k is spring constant of each spring then total spring constant of all the four springs in parallel is,
`k_(p) = 4k`
Now, `Mg = k_(p)x`
`Mg = 4kx`
`therefore k = (Mg)/(4x) = (3000xx10)/(4xx 0.15)`
`therefore k = 5 xx 10^(4) N"/"m`.
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