How Do You Calculate the Spring Constant for a Car's Shock Absorbers?

[Bearbull24.5]

Homework Statement

A car with bad shock absorbers bounces up and down with a period of 1.81 s after hitting a bump. The car has a mass of 1380 kg and is supported by four springs of equal force constant k. Determine a value for k.
Answer in units of N/m.

Homework Equations

T=2pi/w
T=1.81 s

w^2=k/m

The Attempt at a Solution

I solved for w in the above equation and got 11.372 as my answer. I then plugged it into the second equation and solved for k. I got an answer of 178,482.6366 which I immediately plugged in and got wrong. I then divided it by 4 thinking that would work. Nope got it wrong

 

[MissPenguins]

I did the same thing. I rearranged the equation and got k = (2pi/T)² * m. And I got 101806.5992 for mine, and got it wrong. ?? Someone please help. Thanks. ;)

 

[jamesrc]

Bearbull24.5, I believe you solved for the frequency incorrectly (when you solved for w as a function of T, did you end up multiplying 2pi by T or dividing 2pi by T; which should you have done)?

And further, while you were supposed to divide by 4, you should have an understanding of why that is the case. The car is supported by 4 equal springs with spring constant k - these springs are in parallel, meaning that for a given force (the weight of the car), all 4 springs will move down the same amount. If you're looking at the natural frequency of this system, the total spring constant is 4*k. So w^2=4k/m. The rest of the problem is algebra and arithmetic.

MissPenguins, you've made an arithmetic error and forgotten about the factor of 4 described above.

 

[MissPenguins]

Bearbull24.5, I believe you solved for the frequency incorrectly (when you solved for w as a function of T, did you end up multiplying 2pi by T or dividing 2pi by T; which should you have done)?

And further, while you were supposed to divide by 4, you should have an understanding of why that is the case. The car is supported by 4 equal springs with spring constant k - these springs are in parallel, meaning that for a given force (the weight of the car), all 4 springs will move down the same amount. If you're looking at the natural frequency of this system, the total spring constant is 4*k. So w^2=4k/m. The rest of the problem is algebra and arithmetic.

MissPenguins, you've made an arithmetic error and forgotten about the factor of 4 described above.

Alright, I figured it out and got the right answer. Thanks. ;)

 

[Bearbull24.5]

I multiplied 2pi by T

 

[Bearbull24.5]

Got it