Frequency of a suspension spring

Question

Four identical springs used as part of a car's suspension system, one on each wheel. The springs compress by 6 cm when the weight of the 1900 kg car is applied to them.

a) What is the spring constant of each of the springs?

b) With what frequency will the suspension bounce if given a jolt?

c) If the springs are chopped in half (which will double the spring constant) with what frequency will the suspension bounce now?

Answer 1

a) the spring constant for each spring = k = force/ deltax = 1900g/.06=3.11E5 N/m

b) 4 springs supporting the car acting in parallel and the equivalent constant = 1.24E6 N/m

c) the frequency of oscillation - w=sqrt(k/M) = sqrt(1.24E6/1900)= 25.6 rad/sec ... f= 4.07 Hz

d) reducing the length of each spring increases it's constant ... thus k = 3.11E5 *2= 6.22E5 N/m and the new frequency = sqrt(4*6.22E5/1900)= 36.2 rad/sec = 5.76 Hz