Oscillations in a driven spring

[entropy1]

If I have a spring with resonance frequency f_res and I drive it with frequency f_drive, the spring will oscillate in a superposition of two frequencies, right?

Which frequencies are they?

 

[mfb]

If you keep driving it with the same amplitude it will oscillate with f_drive.

 

[entropy1]

If you keep driving it with the same amplitude it will oscillate with f_drive.

Will the spring's oscillation vary in amplitude (if de driver amplitude is constant)?

 

[mfb]

Why would you expect any variation?

 

[entropy1]

Why would you expect any variation?

I think because of the resonance; the spring tends toward it. For instance: if f_drive=f_res+d with d a small number, the spring's resonance frequency will interfere with the driver's frequency and produce a slow oscillation f_res-f_drive I suspect. I recall having seen this at high school but I'm not sure. It is like the spring's phase aligning with the driver's phase and then run out of phase and run back in it again. Is this correct?

That would be a modulation I guess.

 

[Dr.D]

Motion at the natural frequency is associated with the homogeneous solution of the ODE. Even if it is not included in the mathematical formulation, in reality it will die away due to internal friction and also windage.

The steady solution is due solely to the excitation and will occur at the excitation frequency only. If the excitation is close to the natural frequency, the amplitude of the steady state solution will be quite large. This is what is known as resonance.