The shock absorbers in the suspension system of a car are in such bad shape that they have no effect on the behavior of the springs attached to the axles. Each of the identical springs attached to the front axle supports 312 kg. A person pushes down on the middle of the front end of the car and notices that it vibrates through five cycles in 3.2 s. Find the spring constant of either spring.
The period of a spring is given by the formula: T 2π*sqrt(m/k), where m is the mass on the spring and k is the spring constant. Since we need to solve for k, we do some rearranging to get: k (4π^2*m) / (T^2) If it goes through 5 cycles in 3.2 seconds, then the period is 3.2 / 5 0.64s. Now, we have all the numbers we need to plug into the equation. k (4π^2 * 312) / (0.64^2) 30071 N/m
