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From: Greg Heath on 22 Apr 2010 10:23
On Apr 22, 6:49 am, Rune Allnor <all...(a)tele.ntnu.no> wrote:
> On 22 apr, 11:43, "rsk" <kalerahul(a)n_o_s_p_a_m.yahoo.com> wrote:
>
>
>
>
>
> > Sorry for touching this after long time. First of all thank you all for
> > answering my questions eventhough they might be trivial for you.
>
> > Here is a followup question
>
> > Talking about response of a spring mass system to the forced
> > excitation(classical 1 degree of freedom problem in vibration), if I excite
> > a system at 10 Hz, it will oscillate at 10 hz. In case of developing linear
> > vibration theory, we assume that the excitation is a periodic SINE.
>
> > Let's consider two cases,
> > case 1) I excite this spring mass by the force that has only one cycle of
> > sine wave upto 1 sec, with amplitude 1 and rest zero upto 10 sec
> > case 2) I excite this spring mass by the force that has amplitude 1 with
> > sine curve of frequency 1 hz upto 10 sec(that means continuous sine)
>
> > Referring to all our discussion below, case 1 is similar to zero padded
> > sine wave
>
> No, it isn't. The above example is a physical system that is governed
> by the laws of physics. Pick up a physics textbook and learn how
> to solve the associated differential equations.
>
> There is no relation between your example and the FFT.

Not exactly.

1. Solve the ODE for both cases.
2. Take the fft of each solution and compare the spectra.

Hope this helps.

Greg

From: Clay on 22 Apr 2010 10:30

>
> However, the response of the spring mass will be different in case 1 and
> case 2 if we look into time domain. In case 1, it will also have transient
> response due to its mode. In case 2, it will be "forced" to vibrate at 1
> Hz.
>
> In such a case, if I want to analyze it in the frequency domain, I will get
> same response in case 1 and case 2 because the input frequency spectrum
> will be same.
>
> How do I justify this?
>
> Thanks
>
> Rahul
>

Hello Rahul,

As Rune suggests, actually solve the DEQ. What you need to notice is
the resonant frequency shifts slightly due to the dampening term.
Also the frequency content of a modulated (by the transient envelope)
sine wave is more than that of the sine wave alone. To solve the
driven case either use MUC or use Laplace transforms - they are
beautiful for this.

Clay








From: Rune Allnor on 22 Apr 2010 06:49
On 22 apr, 11:43, "rsk" <kalerahul(a)n_o_s_p_a_m.yahoo.com> wrote:
> Sorry for touching this after long time. First of all thank you all for
> answering my questions eventhough they might be trivial for you.
>
> Here is a followup question
>
> Talking about response of a spring mass system to the forced
> excitation(classical 1 degree of freedom problem in vibration), if I excite
> a system at 10 Hz, it will oscillate at 10 hz. In case of developing linear
> vibration theory, we assume that the excitation is a periodic SINE.
>
> Let's consider two cases,
> case 1) I excite this spring mass by the force that has only one cycle of
> sine wave upto 1 sec, with amplitude 1 and rest zero upto 10 sec
> case 2) I excite this spring mass by the force that has amplitude 1 with
> sine curve of frequency 1 hz upto 10 sec(that means continuous sine)
>
> Referring to all our discussion below, case 1 is similar to zero padded
> sine wave

No, it isn't. The above example is a physical system that is governed
by the laws of physics. Pick up a physics textbook and learn how
to solve the associated differential equations.

There is no relation between your example and the FFT.

Rune
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