Question

Two people with a combined mass of 134 kg hop into an old car with worn-out shock absorbers. This causes the springs to compress by 8.50 cm . When the car hits a bump in the road, it oscillates up and down with a period of 1.62 s .

Find the total load supported by the springs in kg.

Find the mass of the car in kg.

Answer 1

Weight of the two people = 134 * 9.8 = 1313.2 N

Compression because of this weight = 8.5 cm = 0.085 m

Therefore spring constant k = 1313.2/0.085 =15449.4118 N/m

a)Time period T = 1.62 s
Let M = total load supported by the springs.

T = 2 * π * sqrt(M/k)

Or T/(2π) = sqrt(M/k)
Or T²/(4π²) = M/k
Or M = k T²/(4π²) = 15449.4118*1.62^2 / ( 4*3.14^2) =1028.07001 kg answer

b) Mass of the car = total load - mass of the two people
= 1028.07001 - 134
= 894.07001 kg​ answer