The shock absorbers in an old car with mass 1160 kg are completely worn out. When a 970 N person climbs slowly into the car, it deforms 3.0 cm. The car is now towed down the road (with the person inside). The car hits a bump, and starts oscillating up and down with an amplitude of 6.4 cm.
Model the car and person as a single body on a spring and find the period and frequency of oscillations.

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Explanation:

The problem can be modelled as a vertical mass-spring system exhibiting a simple harmonic motion. The spring constant is:

The angular frequency is:

The frequency and period of oscillations are, respectively:

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wavelength divides in half and speed stays the same.