A shock absorber is designed to quickly damp out the oscillations that a car wou

Question

A shock absorber is designed to quickly damp out the oscillations that a car would otherwise make because it is suspended on springs. Part A Part complete Find the period of oscillation of a 1680-kg car that is suspended by springs that make an effective force constant of 6.15×104N/m. Express your answer to three significant figures and include appropriate units. 1.04 s Previous Answers Correct Part B Find the damping constant b that will reduce the amplitude of oscillations of this car by a factor of 6.00 within a time equal to half the period of oscillation. Express your answer to three significant figures in kg/s. nothing kgs

Explanation / Answer

Part A -

The expression for the period of a spring-mass system is given by -

T = 2*pi*sqrt(m / k) = 2*3.141*sqrt(1680 / 61500) = 1.038 s

Taking approximation, the period T = 1.04 s

Part B -

Use the expression for the damping constant b -

x = A/6.0 = A*e^(-bt / 2m)
where t = ½*1.04 s = 0.52 s

and m = 1680 kg

Canecel 'A' from both sides -

e^(-b*0.52 / 2*1680) = 1/6 = 0.167

-b*0.52 / 2*1680 = ln(0.167) = -1.792

=> b = (1.792 x 2 x 1680) / 0.52 = 11579 kg/s

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