# Car Suspension, sinusoidal road input

1. Oct 10, 2009

### exidez

1. The problem statement, all variables and given/known data
The question extends more than this but this is where I have difficulty.

An uneven road surface is modelled by a sinusoid with amplitude 25mm and the car is driven at 100km/hr. Use the bode plot calculate earlier to obtain and explain the steady state force response when the road period is:
a. 10m
b. 1m

2. Relevant equations

My problem is that i don't know what to use for angular frequency!

The car suspension looks like this
http://img27.imageshack.us/img27/2193/matlapassig2fig.jpg [Broken]

The transfer function looks like this:

$$Y(S)=F(S)\frac{sm_{u}ck+k_{t}}{s^{4}(m_{u}m_{s})+s^{3}(cm_{s}+cm_{u})+s^{3}(m_{s}k+m_{s}k_{t}+m_{u}k+s(ck_{t})+kk_{t}}$$

Bode diagram is below:
http://img223.imageshack.us/img223/7718/bode.jpg [Broken]

3. The attempt at a solution

so if the road surface is 25mm in amplitude and the period of the sinusoidal is 10m. The car is traveling at 100kmph so this is 27.777m/s. This means the car completes one cycle of the road in 0.36 seconds.
f = 0.36 Hz
$$\omega = 2* \pi *f = 2.26 rad/sec$$

From here i just use the bode plot to find amplitude and phase. This, from what i believe, means the height the driver will move and the delay...

\\OR

being that the road period is 10m, do i just use this:
$$\omega = \frac{2* \pi }{10} = 0.63 rad/sec$$

Can someone please verify that i am calculating the correct angular frequency. I think my first method is correct, but i just want to make sure.

Last edited by a moderator: May 4, 2017
2. Oct 12, 2009

### Staff: Mentor

One cycle in 0.36 seconds would be the period. How do you get the frequency in Hz from the period in seconds?