Oscillations in a driven spring

In summary, when a spring with resonance frequency fres is driven with frequency fdrive, it will oscillate with a superposition of two frequencies: fdrive and fres. The amplitude of the oscillation will depend on the amplitude of the driving force, with higher amplitudes resulting in larger oscillations. The oscillation will be steady at the excitation frequency, but if the excitation frequency is close to the spring's resonance frequency, the amplitude of the oscillation will be significantly increased, known as resonance. This is due to the alignment of the spring's phase with the driver's phase, resulting in a slow oscillation. However, this steady state solution will eventually die away due to internal friction and windage.
  • #1
entropy1
1,230
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If I have a spring with resonance frequency fres and I drive it with frequency fdrive, the spring will oscillate in a superposition of two frequencies, right?

Which frequencies are they?
 
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  • #2
If you keep driving it with the same amplitude it will oscillate with fdrive.
 
  • #3
mfb said:
If you keep driving it with the same amplitude it will oscillate with fdrive.
Will the spring's oscillation vary in amplitude (if de driver amplitude is constant)?
 
  • #4
Why would you expect any variation?
 
  • #5
mfb said:
Why would you expect any variation?
I think because of the resonance; the spring tends toward it. For instance: if fdrive=fres+d with d a small number, the spring's resonance frequency will interfere with the driver's frequency and produce a slow oscillation fres-fdrive 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.
 
Last edited:
  • #6
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.
 

Related to Oscillations in a driven spring

1. What is an oscillation in a driven spring?

An oscillation in a driven spring is a repetitive back-and-forth motion of a spring that is caused by an external force or driving force. This motion is characterized by a constant amplitude and a constant frequency.

2. What causes oscillations in a driven spring?

Oscillations in a driven spring are caused by an external force or driving force acting on the spring. This force can be applied through various means, such as a hand, a motor, or a magnetic field.

3. How does the frequency of the driving force affect the oscillations in a driven spring?

The frequency of the driving force has a direct impact on the frequency of the oscillations in a driven spring. When the frequency of the driving force is equal to the natural frequency of the spring, resonance occurs and the oscillations will reach their maximum amplitude.

4. What is the difference between damped and undamped oscillations in a driven spring?

Damped oscillations in a driven spring occur when there is a dissipative force acting on the spring, causing the amplitude of the oscillations to decrease over time. Undamped oscillations, on the other hand, occur when there is no dissipative force and the amplitude of the oscillations remains constant.

5. How can I calculate the period of oscillation in a driven spring?

The period of oscillation in a driven spring can be calculated using the equation T = 2π√(m/k), where T is the period, m is the mass of the object attached to the spring, and k is the spring constant. This equation assumes that the oscillations are undamped and the driving force is at the resonant frequency.

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