Oscillator with and without damping - Need help please

In summary, the problem involves finding the frequency and ratio of successive amplitudes for an oscillator with natural frequency ω, consisting of a mass on a spring on a frictionless horizontal table for x<0 and a table with friction and an effective damping constant K for x>0. The solution will require considering the two sides of the table separately and using different equations for the motion in each region. Assistance with solving this problem would be greatly appreciated.
  • #1
Fjolvar
156
0
An oscillator with natural frequency ω consists of a mass on a spring positioned on a horizontal table. The table is frictionless for x<0 but has friction for x>0 and an effective damping constant K on that side of the table. Find the frequency of this oscillator and the ratio of successive amplitudes. Assume K<ω (Under-damping).
Relevant equations
x=C*cos(ωt) [Eqn of motion w/o damping] when x<0
x=Ce-Kt cos(ωdt) [Under-damping eqn of motion] when x>0Well it seems there will be two parts of the problem for each side of the table, which means it will probably be one quantity plus another. Any help getting started on this problem would be greatly appreciated. Thank you in advance.
 
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  • #2
It won't be simply the sum of the two. It will consist of alternate pieces of the graphs of the two. We must consider the time intervals in which x>0 & x<0 separately.
 
  • #3
Any others? I don't really think I need to use the graph on this one.
 
  • #4
I've been stuck on this problem for a few days. I just can't see how to reduce it to one equation..
 
  • #5
Any ideas? Class will be starting relatively soon and I've still yet to figure this one out. Any help much appreciated.. thanks.
 

1. What is an oscillator?

An oscillator is a physical system that exhibits repetitive motion around a central equilibrium point. Examples of oscillators include springs, pendulums, and electronic circuits.

2. What is damping in an oscillator?

Damping is the process of reducing the amplitude of an oscillator's motion over time. This is usually achieved through the dissipation of energy, such as through friction or resistance.

3. How does damping affect an oscillator's behavior?

Damping can change the frequency, amplitude, and stability of an oscillator. In a damped oscillator, the amplitude of the oscillations decreases over time and the system reaches equilibrium faster compared to an undamped oscillator.

4. What is the difference between an oscillator with and without damping?

An oscillator without damping will continue to oscillate at a constant amplitude indefinitely, while an oscillator with damping will eventually come to a complete stop due to the loss of energy. Additionally, the frequency of an undamped oscillator remains constant, while the frequency of a damped oscillator decreases over time.

5. How can I calculate the damping ratio of an oscillator?

The damping ratio of an oscillator can be calculated by dividing the damping coefficient (b) by the critical damping coefficient (bc). The critical damping coefficient is equal to 2 times the square root of the mass (m) multiplied by the spring constant (k).

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