How Does Archimedes' Principle Affect Damping in Harmonic Oscillations?

This can lead to a change in the frequency and period of the oscillations as well.In summary, the conversation discusses the influence of the Archimedes' principle of buoyancy on a mass spring system that is dampened by a small steelball in a soap mixture. The buoyancy force, which acts in a vertical direction, can increase the damping effect in the system and affect the curve of harmonic oscillation depending on its magnitude and direction.
  • #1
InGolf
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Hi, I'm trying to build up a mass spring system, which is damp by a small steelball lowered into a buck containing soap mixture. Where the viscosity has been measured and we have calculated the flow arround the ball to be rather laminar (Reynold<1). But our data shows a damping around the double of our theoretical. My question is which influence will the Archimedes' principle of buoyancy have on our steelball and damping? Can the ekstra damping be explained by this force? And how will the buoyancy effect curve af the damp harmonic oscillation when it's only a force of one direktion..?
 
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  • #2
The buoyancy force is a result of the Archimedes' principle, which states that an object immersed in a fluid will experience a buoyant force equal to the weight of the fluid displaced. This force acts in a vertical direction, according to the direction of gravity. Since the steelball is lowered into a buck containing soap mixture, it will be subject to this buoyant force. The buoyancy force can increase the damping effect in the mass spring system due to the additional force acting on the steelball, resulting in a higher damping coefficient.The impact of the buoyancy force on the curve of harmonic oscillation will depend on the magnitude and direction of the force. If the force is pointing in the same direction as the oscillation, it will reduce the amplitude of the oscillations. However, if the force is pointing in the opposite direction, it will increase the amplitude of the oscillations.
 

1. What causes damped harmonic oscillations?

Damped harmonic oscillations are caused by the presence of a damping force, which is a resistive force that opposes the motion of the oscillating system. This force can be due to factors such as friction, air resistance, or resistance in an electrical circuit.

2. How is damping ratio related to damped harmonic oscillations?

The damping ratio is a measure of the amount of damping in a system. It is defined as the ratio of the actual damping coefficient to the critical damping coefficient. A higher damping ratio means a higher level of damping, which results in quicker decay of the oscillations.

3. What is the difference between underdamped, critically damped, and overdamped oscillations?

In underdamped oscillations, the damping force is not strong enough to bring the system to rest, resulting in oscillations that gradually decrease in amplitude. Critically damped oscillations occur when the damping force is just enough to bring the system to rest in the shortest time possible. Overdamped oscillations occur when the damping force is too strong, causing the system to return to equilibrium without any oscillations.

4. How do damped harmonic oscillations differ from simple harmonic oscillations?

Simple harmonic oscillations occur when there is no damping force present, resulting in a system that oscillates indefinitely with a constant amplitude and frequency. Damped harmonic oscillations, on the other hand, experience a decrease in amplitude and frequency due to the presence of a damping force.

5. What are some real-world applications of damped harmonic oscillations?

Damped harmonic oscillations can be observed in many real-world systems, such as the suspension of a car, the motion of a pendulum, and the vibration of a guitar string. They are also important in engineering applications, such as in shock absorbers, electrical circuits, and mechanical systems that require controlled vibrations.

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