Solving second order differential equation?
Solving second order differential equation?
(OP)
I would like to solve a second order differential equation that represents a spring mass damper system that has an external acceleration applied to it.
I need to know the displacement over time output curve x(t). The input acceleration curve Gz(t)is a data set from experiment.
I have attached a picture (Mathcad Function.jpg) of my Mathcad sheet with the function to solve and a plot of the input acceleration trace.
Is it possible to solve this equation for x(t)?
If so I am not that familiar with Mathcad to know exactly how to do this, any help would be appreciated.
Thanks.
I need to know the displacement over time output curve x(t). The input acceleration curve Gz(t)is a data set from experiment.
I have attached a picture (Mathcad Function.jpg) of my Mathcad sheet with the function to solve and a plot of the input acceleration trace.
Is it possible to solve this equation for x(t)?
If so I am not that familiar with Mathcad to know exactly how to do this, any help would be appreciated.
Thanks.
RE: Solving second order differential equation?
Peter Nachtwey
Delta Computer Systems
http://www.deltamotion.com
RE: Solving second order differential equation?
If I use the solve block and instead of submitting Gz(t) as my input acceleration I just use a single value I can obtain a solution for x(t). However If I input the input acceleration as a variable Gz(t) as I need to I cannot obtain a solution.
Accorading to the pendulum help example I believe I need to enter the solve blaock in this fashion Odesolve([vector], x, b, [step]) for my solution to be calcualted by I do not know how to ue this despite my best efforts.
I am not sure what to do with the [vector] part and the help is not particulalry helpful in this regard.
Do you have any examples you may be able to guide me with?
Thanks Peter.
RE: Solving second order differential equation?
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This example is a little more than what you asked for because I show how to control the mass on a spring. All you are interested in is page 4/24 and this x=A*x+B*u
I made this example to show other how important the second derivative gain is for damping and controlling an under damped system. I was comparing my PID solution with another persons best PI solution.
Peter Nachtwey
Delta Computer Systems
http://www.deltamotion.com
RE: Solving second order differential equation?
I have struggled to follow your advice relating to my problem. I believe my methodology is correct however I continually receive a Mathcad error message stating:
"the return value of this function must match the problem size"
I am not sure what this means and would be highly greatful if you could offer any further assistance. I have attached my Mathcad file to this post, I was wondering if you could take a quick look at it and give me any advice that you would kindly offer.
Thankyou again for your assistance.
Regards,
Rich.