A car has a unibody-type frame and is supported by four suspension springs, each with
a force constant of 36100 N/m. The combined mass of the car’s frame and everything
inside it (the engine, the seats, the passengers,
etc.) is 1270 kg. Because of worn-out shockabsorbers, the car vibrates up and down every
time it is driven over a pothole.
What is the frequency of this vibration?
Answer in units of Hz
To calculate the frequency of the car's vibration, we can use the equation for the natural frequency of a mass-spring system. The formula is:
f = 1 / (2π) * √(k / m)
Where:
f = frequency in hertz (Hz)
k = force constant (N/m)
m = mass (kg)
In this case, we are given the force constant (36100 N/m) and the mass (1270 kg). Plugging these values into the formula, we get:
f = 1 / (2π) * √(36100 / 1270)
Simplifying the equation further:
f = 1 / (2π) * √(28.346)
Using a calculator, we find:
f ≈ 1.333 Hz
Therefore, the frequency of the car's vibration is approximately 1.333 Hz.