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Clue. When you are in a hole, stop digging. In the world of vehicle dynamics it is very common to assume that springs and shocks are massless. For example a linear spring in ADAMS is represented by an equation that boils down to f=k.x its mass is lumped into the sprung and unsprung mass. I answered the OP's question exactly. If he asked the wrong question he can ask another. So, what's your answer ?
He asked for the equation of motion. Please describe what the acceleration is in your equation.
You can't.
There is only one equation and thats
F=ma+cv+kx.
Yes you do assume springs are massless but they are always connected to a lumped mass-that's what gives the system its degrees of freedom. You can only describe the motion of the mass points.
You should spend less time writing 'smart' condescending replies and more time studying engineering texts.
It would be interesting to know which answer is most useful to the OP.
If he is designing parts he needs to know the dynamics of it (with mass). If he only wants say a simple motion sort of thing, he can work with the kinematics alone.
I can model various proprietary metrics of primary ride on measured road surfaces with an R^2 of 0.8 using my approach. However I'm sure the textbooks will help improve that.
These textbook models are used everywhere from driveline torsional vibration to high speed rotordynamics, valvetrain and geartrain models. Even models with very high non linearity can correlate to within measurement error for up to several kHz.
Your model that only works for a very narrow frequency range and even then does not account for 20% of variability is poor by any standard. And if you try to argue that whatever it is you are predicting is independent of wheel mass I'm not buying it.
The reason your model seems to work is because your suspension excitation frequency is much higher then its natural frequency (I suspect about 2 Hz ? I'm not a suspension guy) and hence the transmissibility is very low. This however constitutes a very particular case - it simply won't work at resonance.
Probably just about adequate for designing a wheelie bin.
I didn't say it didn't use mass i said the spring and damper were modelled using the equations given. You are out of your depth. Its a full vehicle adams model, used to predict both steady state handling and limit handling and rollover and now primary ride, all correlated with real vehicle tests. I'll take your advice on accuracy and stick it where it belongs. Let me guess, you've never measured ride on a real car, so you have no idea about test to test variability.
Im not quite sure if you are being deliberately obtuse - if your system has mass ,springs and dampers then the system equation (Newton) is the one I have mentioned. It is valid for any number of degrees of freedom and any form of excitation in either time or frequency domain.
Regardless of the software you are using it will either solve Newton's equations (which obviously involve mass) or the Lagrange method (where kinetic energy is mv^2/2, again dependent on mass).
I'm sure you can use software too bad you can't understant how it works.