Oscillator driving frequencies

[Saado]

I've attached a graph to this post. Why is it that the periodic external frequency applied never starts at 0 on graphs like these?

 

[AlephZero]

It does start at 0 on the graph you posted.
$\omega_A$ is the input frequency (or periodic external frequency). When $\omega_A = 0$, the frequency ratio $\omega_A\omega_0 = 0$.

 

[Saado]

Sorry my bad I meant the amplitude of the oscillations.

 

[AlephZero]

If the force has constant amplitude, at low frequencies the $m\ddot x$ term is small compared with the $kx$ term in the equation of motion, so the amplitude is approximately $F/k$. That is why the amplitude doesn't go to 0 as the frequency goes to 0.

Note, these type of plots can be drawn in different ways, corresponding to different physical situations:

1. The force has constant amplitude, like your attachment
2. The force amplitude is proportional to the frequency
3. The force amplitude is proportional to the frequency squared (for example the unbalanced force on a rotating object)

You can also plot how the velocity, and acceleration of the system changes with frequency.

Most of those plots do go to 0 when the frequency is 0.

 

[PJC01]

The reason that the periodic external frequency applied never starts at 0 on graphs like these is due to the nature of oscillators. Oscillators are systems that exhibit periodic motion and are driven by an external force or frequency. When an external frequency is applied, it causes the oscillator to vibrate at a specific frequency, which is represented on the graph.

However, the initial starting point of the graph is not at 0 because the oscillator needs time to respond to the external frequency and reach its steady-state oscillation. This initial response time is known as the transient response and is shown as the initial rise on the graph before reaching the steady-state oscillation.

In addition, the oscillator may also have an initial phase shift, which causes the starting point of the graph to be shifted from 0. This phase shift can be due to various factors such as the initial conditions of the system or the type of oscillator being used.

In conclusion, the starting point of the graph for oscillator driving frequencies is not at 0 due to the transient response and possible initial phase shift of the oscillator. It is important to consider these factors when analyzing and interpreting data from oscillators.