Force mechanical oscillator and frequency independent?

[hemetite]

i got these question which i do not know how to do...

Qn. In a forced mechanical oscillator, show that the following are frequency independent.

i) the mechanical amplitude at low frequencies.
ii) the velocity amplitude at velocity resonance.
iii) the acceleration amplitude at high frequencies.

how do i start?

i know that the formual for

displacement= F/wZ sin (wt -teta)
where Z= sqrt[ r sq + ((mw - s/w) sq) ]

velocity= F/Zm cos (wt- teta)

how to go about in this question?

 

[Topher925]

Might I ask what subject this is for? I don't think I have ever heard of a "velocity resonance" before. Is this something that needs to be shown mathematically or is it a concept problem?

 

[hemetite]

this is for damped oscillation subject.

not sure...look like a concept problem..but dun think it is so simple...maybe need to derive mathematically...

anyway..here is my answer that i thought it over yesterday..what do you think?

i) displacement amplitude at low frequencies

x= F/wZ sin (wt-teta),
Z=sqrt( r square + (mw - s/w) square),
Z= mechanical impedence of the system

at low frequency, the denominator of F/wZ will make F the numerator the largest.

In Z=sqrt( r square + (mw - s/w) square), when w --> 0. Z= sqrt(r)

so at low frequency, F/wZ, will lead to F/r, which the system be affected much by r(stiffness of the system)..

this is what i get for the first one..