A car has a unibody-type frame and is supported by four suspension springs, each with a force constant of 47100 N/m. The combined mass of the car's frame and everything inside it (the engine, the seats, the passengers, etc.) is 1190 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.

Question

Physics

Santiago Bryant

4 January, 05:46

A car has a unibody-type frame and is supported by four suspension springs, each with a force constant of 47100 N/m. The combined mass of the car's frame and everything inside it (the engine, the seats, the passengers, etc.) is 1190 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.

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Answers (1)

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Desmond George · Answer 1

Frequency = 2Hz

Explanation:

In simple harmonic motion,

Frequency is given by the formula;

f = (1/2π) √ (k/m))

Where,

k is spring constant and

m is mass

Now, the question says there are 4 suspension springs with each having a spring constant of 47100 N/m. Thus, the total amount of spring constant will be;

K_total = 4 x 47100 N/m = 188,400 N/m

Thus, let's now find the frequency since we have m = 1190kg

f = (1/2π) √ (k/m)

f = (1/2π) √ (188400/1190)

f = (1/2π) x 12.5825

f = 0.159149 x 12.5825 = 2 Hz