A car with bad shocks bounces up and down with a period of 1.62 s after hitting a bump.The car has a mass of 1,600 kg and is supported by four springs of force constant k.What is k for each spring?

A) 6,017 N/m
B) 1,504 N/m
C) 1,551 N/m
D) 3,009 N/m
E) 788 N/m

Question

A car with bad shocks bounces up and down with a period of 1.62 s after hitting a bump.The car has a mass of 1,600 kg and is supported by four springs of force constant k.What is k for each spring?
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A) 6,017 N/m
B) 1,504 N/m
C) 1,551 N/m
D) 3,009 N/m
E) ​788 N/m

Quizplus · Accepted Answer

The period of oscillation T is related to the mass m and the spring constant k by the formula T = 2π√(m/k). Solving for k gives k = (4π²m)/(T²). Substituting m = 1600 kg and T = 1.62 s, we find the total k for all springs. Since there are four springs, divide the total k by 4 to find k for each spring, which results in approximately 6,017 N/m.

A Car with Bad Shocks Bounces Up and Down with a Period