Second Order Differential Equations

I do not see any attachments as are referenced. Did I hit my head too hard this morning? I didn't think posting attachments was possible ...

So instead, I will post this link to wikipedia! http://en.wikipedia.org/wiki/Laplace_transform

thank you for the warm welcome - I hope you did not hurt yourself getting up this morning.

another (Guru) user seems to think files can be uploaded !!!!

Yes I have already visited the wikipedia and other relevant sites - but still no joy.

I will try the Fourier method now.

You can copy a portion of a pdf into a graphic file using a screen capture

This requires some fiddling to make it readable... and if it goes on for pages, it is doubly problematic. You can also drop the file in something like dropbox, and provide a link.

thank you for you suggestion.

the pdf is 8/9 pages, so could be a bit awkward taking screen shots etc.

Even though i havent done it before i will try uploading the pdf to a host site with a link.

cheers, derek

You can post your attachments as picture file by clicking on little green camera icon and selecting file...Let's see if you can master this before moving on to more complex issues...welcome to the forum

thank you for the warm welcome.

I had tried as you had suggested, but got a message that the server would now accept MIME ???

Looks like i cannot do this simple ask and perhaps should give up on ode !!!

Multipurpose Internet Mail Extensions (MIME) is an Internet standard that extends the format of email to support:

• Text in character sets other than ASCII
• Non-text attachments
• Message bodies with multiple parts
• Header information in non-ASCII character sets

first of all you cannot tell about the actual equation, by the way it can solve by Laplace transform also web.firat.edu.tr/agulucar/AM/laplaceforengineer.pdf

thank you i will have a look

In order to use a square wave to excite a system, I have always used just one edge to limit it to a step function. Then I differentiate that to get an impulse, and the differentiated output is then the impulse response. Of course, the FFT of the impulse response is easy to calculate. To normalize, divide the output FFT by the input FFT to get the corrected FFT, and that will be the Frequency Response Function (FRF). The transfer function is then the LaPlace Transform of the FRF.

Care must be taken to assure that the edge rate of the square wave is fast enough to excite all modes of the system under test. Also, the duration of the step must be long enough to allow all modes to damp to zero. This usually means that the square wave is a relatively low frequency (i.e. a low repetition rate).

thank you for getting back.

i would really like to upload the laplace pdf for comment because i think i am almost there with it and i am only missing/overlooking something minor.

i will bear you solution in mind if i cannot solve with the laplace transform.

thanks, derek

There is more than one way to skin a cat. I prefer to use the Bode plot. The first order plot is standard in renormalized frequencies. For second order you add two plots together. Phase response is standard per section. You read out every harmonic out, amplitude and phase delay for each.

I know, it is not standard here. But I like the graphic method's directness.

thank you for getting back.

like before i would like to progress the laplace method although i have plotted the bode plot of the freq. response and also the step response function and considered damping.

thanks derek