The body of a 1258 kg car is supported on a frame by four springs. The spring constant of a single spring is 1.31 × 104 N/m. Four peo- ple riding in the car have a combined mass of 230 kg. When driven over a pothole in the road, the frame vibrates and for the first few seconds the vibration approximates sim- ple harmonic motion.

What is the period of vibration of the car? Answer in units of s.

To find the period of vibration of the car, we need to use the formula:

T = 2π√(m/k)

Where:
T is the period of vibration.
m is the effective mass.
k is the spring constant.

In this case, the effective mass (m) is the sum of the mass of the car (M) and the mass of the people (m_p), since they all contribute to the vibrations:

m = M + m_p

Given:
Mass of the car, M = 1258 kg
Combined mass of the people, m_p = 230 kg
Spring constant, k = 1.31 × 10^4 N/m

Substituting the values into the formula:

m = 1258 kg + 230 kg = 1488 kg

T = 2π√(1488 kg / (1.31 × 10^4 N/m))

Now, we can calculate the period of vibration (T).