Understanding Resonance Frequency Decrease in Oscillation Systems

[Wen]

In an Oscillating system,as damping increases, the amplitude of the system at the resonance frequency decrease and the resonance frequency also decreased. However why does the reasonce freq decrease? I know how to solve for the new amplitude and ang. freq. mathematically but i do not know how to explain the decrease in resonant freq. qualitatively?
Can someone just explain it to me?

 

[quantumdude]

Take a look at the general expression for the damped resonant frequency $\omega_d$.

$$\omega_d=\sqrt{\frac{k}{m}-\frac{b^2}{4m^2}}$$

Note that $\frac{k}{m}$ is the undamped resonant frequency $\omega_0$. If $\omega_0$ is taken to be a constant then $\omega_d$ is seen to be a decreasing function of the damping coefficient $b$.

 

[lightgrav]

damping is friction; a damped oscillator moves slower than an undamped one.
If the oscillator travels slower, it takes longer time to complete an oscillation.

 

[Wen]

I'm sorry but Is it so simple? So the phase difference doesn't matter? Why is it known as a mechanical RESPONSE?

 

[Astronuc]

I'm sorry but Is it so simple? So the phase difference doesn't matter? Why is it known as a mechanical RESPONSE?

Simple harmonic motion was known from observations of mechanical systems, e.g. springs, long before electricity was discovered.

 

[quantumdude]

damping is friction; a damped oscillator moves slower than an undamped one.
If the oscillator travels slower, it takes longer time to complete an oscillation.

He's not asking why the system moves slower, he's asking why the resonance was displaced.

Wen: I'm sorry but Is it so simple? So the phase difference doesn't matter? Why is it known as a mechanical RESPONSE?

Astronuc: Simple harmonic motion was known from observations of mechanical systems, e.g. springs, long before electricity was discovered.

He's not talking about electricity. Phase differences can crop up in any system that is described with periodic functions, as this one is.

 

[quantumdude]

So the phase difference doesn't matter?

Which phase difference? You didn't specify a forcing function, so all we have here is the natural response.

Why is it known as a mechanical RESPONSE?

Why is what known as a mechanical response? The reason I ask is that the mechanical response for an oscillator is typically a time-varying function of position. But you never referred to such a thing, so I don't know what you mean by "it" in that question.

 

[Wen]

Sorry i wasn't specific, what i was asking was that an oscillating system, undergoing forced oscillation by an external periodic force and damping increased. So why did the resonant freq of the enternal force decreases( as seen a shift to the left in the graph)?
Someone mentioned that resonance was displaced? So my qn was why is it displaced to the left on the graph, when damping increases.

 

[quantumdude]

Sorry i wasn't specific, what i was asking was that an oscillating system, undergoing forced oscillation by an external periodic force and damping increased.

That's OK, because it doesn't matter if your oscillator is forced or not. The resonant frequency will be the same either way. Remember that the resonant frequency is found by solving for the natural (that is, unforced) response.

So why did the resonant freq of the enternal force decreases( as seen a shift to the left in the graph)?
Someone mentioned that resonance was displaced? So my qn was why is it displaced to the left on the graph, when damping increases.

I answered that in my first reply.