The body of a 1285 kg car is supported on a

frame by four springs. The spring constant of
a single spring is 2.80 × 104 N/m. Four people
riding in the car have a combined mass
of 275 kg. When driven over a pothole in
the road, the frame vibrates and for the first
few seconds the vibration approximates simple
harmonic motion.
What is the period of vibration of the car?
Answer in units of s.

To determine the period of vibration of the car, we need to use the equation:

T = 2π√(m/k)

where T is the period, m is the effective mass, and k is the spring constant.

The effective mass (m) is the sum of the car's mass (M) and the combined mass of the four people (m_p).

m = M + m_p

Given:
M = 1285 kg (car's mass)
m_p = 275 kg (combined mass of four people)
k = 2.80 × 10^4 N/m (spring constant)

First, let's calculate the effective mass:

m = M + m_p
m = 1285 kg + 275 kg
m = 1560 kg

Now, we can substitute the values into the equation for the period:

T = 2π√(m/k)
T = 2π√(1560 kg / 2.80 × 10^4 N/m)

Now, let's calculate the square root:

T = 2π√(5.571428571428571 * 10^-2 kg/N)

Finally, calculate the period T:

T = 2π * 0.74630255212 s
T ≈ 4.69 s

Therefore, the period of vibration of the car is approximately 4.69 seconds.