Question

6. The shock absorbers of an old car with a mass of 1300 kg are worn. When a 680 N person slowly climbs into the car at its center of gravity, the car drops 5.0 cm. When the car, with the person on board, falls into a hole, it begins to oscillate vertically in a simple harmonic movement. Consider the car and the person as one body (only one mass) in a single spring and calculate (a) the period and (b) the oscillation frequency

Answer 1

we can find the spring constant

F = kx

k = F / x

here F is weight of the person

k = 680 / 0.05

k = 13600 N/m

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the time period is given as

T = 2$\pi$ * sqrt ( m / k)

here m = ( 680 / 9.8) + 1300 = 1369.38 kg

so,

T =  2$\pi$ * sqrt ( 1369.38 / 13600)

T = 1.993 sec

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frequency , f = 1 /T

f = 0.5015 Hz