When a 82.0 kg. person climbs into an 1800 kg. car, the car's springs compress vertically 1.7 cm. What will be the frequency of vibration when the car hits a bump

The total mass is 1800+85= 1885 kg.

If there are 4 springs, the mass per each spring is
m = 1885/4 =4705 kg.
Hook’s law
F= - kx,
k•x =m•g,
k=m•g/x = 4705•98/0.017 =2.7•10^6 N/m
Angular frequency
ω = sqrt(k/m) = sqrt(2.7•10^6/1885) = 37.9 rad/s.
f = ω/2• π =6 Hz

The total mass is 1800+85= 1885 kg.

If there are 4 springs, the mass per each spring is
m = 1885/4 =471.25kg.
Hook’s law
F= - kx,
k•x =m•g,
k=m•g/x = 471,25•9.8/0.017 =2.7•10^5 N/m
Angular frequency
ω = sqrt(k/m) = sqrt(2.7•10^5/1885) = 12 rad/s.
f = ω/2• π =1.9Hz

that is what I did and I am still getting my problem wrong

Now it has to be correct...

m1 = 82 kg, m2 =1800 kg,
x =1.7 cm = 0.017 m.

It’s important that only the added weight that causes
the spring to compress 1.7 cm.
k = m1•g/x = 82•9.8/0.017=4.73•10^4 N/m,
m = m1 +m2 =1800+85= 1885 kg.
The total weight will oscillate.
ω = sqrt(k/m) =
= sqrt(4.73•10^4 /1885) = 5 rad/s.
f = ω/2• π = 5/2• π = 0.8 Hz

To find the frequency of vibration when the car hits a bump, we need to use the formula for the frequency of a mass-spring system:

\[ f = \frac{1}{2\pi} \sqrt{\frac{k}{m}} \]

Where:
- \( f \) is the frequency of vibration,
- \( k \) is the spring constant, and
- \( m \) is the mass of the system.

To calculate the spring constant, we can use Hooke's law:

\[ F = kx \]

Where:
- \( F \) is the force applied to the spring, and
- \( x \) is the displacement of the spring from its equilibrium position.

Given that the person's weight is 82.0 kg and the car's springs compressed vertically by 1.7 cm, we can determine the force applied to the spring:

\[ F = mg \]

Where:
- \( m \) is the mass of the person, and
- \( g \) is the acceleration due to gravity (approximately 9.8 m/s^2).

Substituting the values, we have:

\[ F = 82.0 \, \text{kg} \times 9.8 \, \text{m/s}^2 \]

Next, we need to calculate the spring constant using the formula \( k = \frac{F}{x} \), where \( x \) is the displacement of the spring:

\[ k = \frac{F}{x} = \frac{82.0 \, \text{kg} \times 9.8 \, \text{m/s}^2}{0.017 \, \text{m}} \]

After calculating the value of \( k \), we can substitute it and the mass of the car (\( m = 1800 \, \text{kg} \)) into the frequency formula to find the frequency of vibration.