Homework Help: Amplitude of oscillations depends on the amount of damping?

1. Jan 8, 2009

nokia8650

Which one of the following statements about an oscillating mechanical system at resonance, when it oscillates with a constant amplitude, is not correct?

A The amplitude of oscillations depends on the amount of damping.
B The frequency of the applied force is the same as the natural frequency of oscillation of the system.
C The total energy of the system is constant.
D The applied force prevents the amplitude from becoming too large.

The answer is A. Can someone please explain why A in incorrect, and why D is correct?

Thank you very much.

2. Jan 8, 2009

Redbelly98

Staff Emeritus
Re: Resonance

That's weird, I would agree with you that statement A is correct, and D is wrong.

3. Jan 8, 2009

turin

Re: Resonance

The applied force overcomes the damping. The damping prevents the oscillation from becoming too large. If there were no damping, the applied force would cause the oscillation to grow without bound. If you're an engineer, that would be a pole on the imaginary axis; the damping shifts the poles into the left-half plane. What I find wierd is that A also is correct: if the damping is stronger, ceteris paribus, then the oscillations should be smaller. In other words, the further into the left half plane, the weaker and more spread out the resonance peak will be.

4. Jan 14, 2009

mharaghi

Re: Resonance

the A is incorrect because it says when the oscillations are constant, which means we arein the steady-state response. Damping shows its effects in the transient time, not in the steady-state time, so the amplitude has become larger and larger, and it became constant eventually, and afterwards there will be no effect from damping.

it might have, in fact, damping effects depending on the frequency of oscillations, where the system is unable to reach the utmost value.

Last edited: Jan 14, 2009
5. Jan 14, 2009

turin

Re: Resonance

Wrong. The damping coefficient appears in the denominator of the steady-state response. Larger damping coefficient in denom. leads to decreased amplitude.

6. Jan 14, 2009

Redbelly98

Staff Emeritus
Re: Resonance

I'm with turin on this. If damping is present, and the mass is moving, then damping must be showing it's effects. The damping force is
- β v​
so as long as v≠0, the damping has an effect.

7. Jan 15, 2009

mharaghi

Re: Resonance

to me, when it is in resonant frequency means it is a positive feedback, and essentially goes unbound. Since it doesn't go unbound (becomes constant), it is limited to some saturation limits. Therefore, the magnitude is dependent on some saturation limits. This saturation can be caused by a very high damping, but might be from somewhere else; however, the shape of the signal is still dependent on the damping.

8. Jan 15, 2009

Redbelly98

Staff Emeritus
Re: Resonance

Well yes, clearly in a real mechanical system there will usually be something preventing the amplitude from exceeding a certain maximum. Either that, or it will simply break when driven beyond some point.

That being said, if the amplitude is below this maximum-- OR if we are talking about a textbook, hypothetical system with no maximum amplitude-- then it will be the damping that limits the amplitude at resonance.

9. Feb 16, 2009

naven8

Re: Resonance

what is resonance?when it occurs?

Last edited: Feb 16, 2009
10. Feb 16, 2009

Re: Resonance

naven8 a system will resonate(vibrate with maximum amplitude) when a forcing frequency matches a natural frequency.Think of pushing someone on a swing.

The amplitude of oscillations depends on the damping and on the applied force and on the system.The thing that is incorrect is the question itself,it is not detailed enough.

11. Feb 16, 2009

naven8

Re: Resonance

In electronic system(circuit) how resonance occur?
how to measure the frequency of a microwave in a wave guide using resonance?

Last edited: Feb 16, 2009
12. Feb 16, 2009

djeitnstine

Re: Resonance

I'm with turin and redbelly on this. D has to be false and A true. Even thinking about it in layman's terms...D is simply counter intuitive.

Also to mharaghi...do some resonance calculations and play around with the damping constant. You will find the amplitude can change drastically with slightly different damping constants