Springs: Simple Harmonic Motion

[TJC747]

A compact car has a mass of 1050 kg. Assume that the car has one spring on each wheel, that the springs are identical, and that the mass is equally distributed over the four springs.

(a) What is the spring constant of each spring if the empty car bounces up and down 2.0 times each second?
(in N/m)

(b) What will be the car's oscillation frequency while carrying four 110 kg passengers?
(in Hz)



I know all the equations for this problem, most centrally Hooke's laws; however, I am having difficulty piecing them all together. Help would be appreciated. Thanks.

 

[ideasrule]

List the equations you know. Which have quantities that are given in the questions?

 

[kerimek]

(a) The spring constant can be calculated using the equation: k = (4π^2m)/T^2, where m is the mass of the car and T is the time for one complete oscillation. In this case, the time for one complete oscillation is 0.5 seconds (since the car bounces up and down 2.0 times each second). Therefore, the spring constant for each spring would be: k = (4π^2 * 1050 kg)/(0.5 s)^2 = 167,400 N/m.

(b) When the car is carrying four 110 kg passengers, the total mass of the car would be 1050 kg + (4*110 kg) = 1490 kg. Using the same equation as above, the oscillation frequency would be: f = 1/T = 1/(2π√(m/k)) = 1/(2π√(1490 kg/167,400 N/m)) = 1.05 Hz.