Answer
See answer.
Work Step by Step
The period for an underdamped oscillation is approximately the same as that for an undamped oscillation. Measure the period of oscillation by pushing down on the car, and then time how long it takes for the car to complete an oscillation (down and then back up to the original position).
Relate the period to the mass and spring constant using equation 11–6a.
$$T=2\pi \sqrt{\frac{m}{k}}$$
Now find the effective spring constant for the entire system.
$$k=m(\frac{2 \pi}{T})^2$$
Each spring supports one-fourth the mass of the car.
$$k_{one\;spring}=\frac{m}{4}(\frac{2 \pi}{T})^2=\frac{m \pi^2}{T^2}$$
