Final answer:
To find the period of vibration of the empty car, we need to understand that the period depends on the mass of the car and the spring constant of the suspension system. While we don't have the spring constant, we can use the proportionality between period and the square root of the mass for our calculations.
Step-by-step explanation:
The question asks about calculating the period of vibration of an empty car using harmonic motion concepts. When passengers enter a car with worn-out shock absorbers, they compress its springs, affecting the car's natural frequency of vibration. The period of oscillation for the loaded car is given, and we need to find the period for the empty car. This can be done by using the formula T = 2π√(m/k), where T is the period, m is the mass, and k is the spring constant. Since the spring constant remains the same and the mass will decrease when the passengers leave the car, the period will be shorter for the empty car.
To find the spring constant (k), we would use the equation F = kx, where F is the force exerted by the mass of the passengers, and x is the compression of the springs. However, since we do not have the value of k or enough data to calculate it, we cannot proceed directly. Instead, we apply the concept that the period is proportional to the square root of the mass. Using the ratio of the masses of the loaded and empty car, we can find the ratio of the periods and then calculate the period for the empty car.