Oscillation with constrained amplitude

In summary, the conversation discusses the behavior of a simple oscillating spring mass system when it is placed on a table with limited amplitude. If the amplitude is constrained to a certain distance, the system can no longer be described as a driven harmonic oscillator. The use of a physics kit is not necessary but can be helpful for understanding these concepts. The effect of external forces, such as the floor, can complicate the behavior of the system and may result in a build-up of energy. This topic is usually studied later on in a physics curriculum.
  • #1
VicomteDeLaFere
2
1
TL;DR Summary
Natural frequency oscillation when constrained: spring mass system on a table restraining amplitude
Hello,

Suppose we have a simple oscillating spring mass system. The natural frequency will excite the system to have infinite amplitude. Suppose then, that we have that system on a table so that amplitude is limited. I'm imagining the high school experiment with the spring mass system on the teacher's table. The teachers always stop before the mass hits the table.

What would the response look like if the table were higher and the oscillation amplitude of the mass was constrained to a certain distance? What if that constrained distance was the resting distance? That is to say, what if the mass naturally, barely rests on the table and there is a driving force at the natural frequency? Would the mass even begin moving?

Thank you (I need to buy a physics kit.)
 
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  • #2
VicomteDeLaFere said:
The natural frequency will excite the system to have infinite amplitude.
This is only true in the idealised case where there are no dissipative forces involved. In a more realistic scenario, amplitude is constrained by the energy loss over one period being equal to the energy put into the system by the driving force.

VicomteDeLaFere said:
What would the response look like if the table were higher and the oscillation amplitude of the mass was constrained to a certain distance? What if that constrained distance was the resting distance? That is to say, what if the mass naturally, barely rests on the table and there is a driving force at the natural frequency? Would the mass even begin moving?
It is difficult to tell exactly what you are imagining. If you restrain the amplitude by an external force, your system will no longer be describable in terms of a driven harmonic oscillator.
 
  • #3
VicomteDeLaFere said:
(I need to buy a physics kit.)
No real need for this. Most of these problems can be solved in your head, although a Physics Kit can be fun.
VicomteDeLaFere said:
amplitude of the mass was constrained to a certain distance
So the mass bumps against the floor? Then it could lose all its Kinetic energy and there would only be one cycles worth of Energy in the system and there would be no build up of energy. If there is an elastic collision with the floor (some bounce), then the mass would rise at a time that the exciting force is not occurring at the right time. The situation is then much more complicated, as @Orodruin says and the simple harmonic oscillator analysis no longer applies. Depending on the details of timing and distances, you could get some energy build up in the system with a very complicated form of motion.
These scenarios are a year or more down the road from SHM in your studies.
 

1. What is oscillation with constrained amplitude?

Oscillation with constrained amplitude refers to a type of motion where an object or system moves back and forth between two points, but is limited in how far it can move from its equilibrium position. This is often seen in pendulums, where the amplitude is constrained by the length of the string or rod.

2. How is the amplitude of oscillation constrained?

The amplitude of oscillation can be constrained in various ways, such as through physical barriers or by using a damping mechanism. For example, in a simple pendulum, the amplitude is constrained by the length of the string or rod. In a damped harmonic oscillator, the amplitude decreases over time due to the presence of a damping force.

3. What is the difference between constrained and unconstrained oscillation?

In unconstrained oscillation, there are no limitations on the amplitude of the oscillation. The object or system can move freely between its maximum and minimum positions. In constrained oscillation, the amplitude is limited in some way, either by physical constraints or by a damping mechanism.

4. What are some real-life examples of oscillation with constrained amplitude?

Some common examples of oscillation with constrained amplitude include pendulums, springs, and musical instruments. In a pendulum clock, the amplitude of the pendulum's swing is limited by the length of the pendulum. In a guitar, the amplitude of the string's vibration is constrained by the length of the string and the placement of frets.

5. How is oscillation with constrained amplitude useful in science and engineering?

Oscillation with constrained amplitude is a fundamental concept in many fields of science and engineering. It is used to model and understand various phenomena, such as the motion of planets, the behavior of electrical circuits, and the dynamics of structures. It also has practical applications, such as in the design of suspension systems for vehicles and the tuning of musical instruments.

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