In a car, there are four wheels that are attached to the body by springs which allow the car to move up and down as it crosses bumps and dips on the road. Each spring supports approximately $\frac{1}{4}$ of the mass of the vehicle. A lightweight car has a mass of $2000kg.$ When an $80-kg$ person sits on the left front fender, this corner of the car dips by about $2cm.$

$1-$ What is the spring constant, $k,$ of this spring?

$2-$ When four people of this mass are in the car, what is the oscillation frequency of the vehicle on the springs?