Understanding Simple Harmonic Motion in a Loaded Floating Log

In summary, the conversation discusses the process of showing that a cylindrical wooden log loaded with lead and floating vertically in water undergoes simple harmonic oscillation. This is achieved by considering the role of gravity and density in finding the equation of motion, which can be modeled as a simple harmonic oscillator. The buoyant force, equal to the difference between the weight of the submerged portion of the log and the displaced water, plays a key role in this motion. The conversation also touches upon finding the value of omega (w) and the possibility of modeling the motion as a spring force.
  • #1
falcon0311
29
0
A cylindrical wooden log is loaded with lead at one end so it floats vertically in water. The submerged part is 2.56 m (called L). I'm supposed to show the oscillation is simple harmonic.

Can someone point me in the right direction? For some reason I'm thinking gravity and density play a big part of find the this equation. After that, I can find the period.
 
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  • #2
Gravity pulls the log down and buoyancy pushes it up. The buoyant force is equal to the difference between the weight of the submerged portion of the log and water that would occupy the same volume. If you work these out correctly your equation of motion should look like a simple harmonic oscillator.
 
  • #3
how would you model this motion? How do you find w(omega). D

Do you model this as a spring force on the object? I have a similar problem and am stuck. Thanks!
 
  • #4
The bouyant force goes like distance submerged. That will push it up, gravity will push it down. Work out the algrebra and get it into a form where you recognize.
 

FAQ: Understanding Simple Harmonic Motion in a Loaded Floating Log

1)

What is Simple Harmonic Motion?

Simple Harmonic Motion (SHM) is a type of periodic motion where an object oscillates back and forth around a central equilibrium position due to a restoring force that is proportional to the object's displacement from that position. It can be described mathematically by a sinusoidal function.

2)

What are the characteristics of Simple Harmonic Motion?

The characteristics of Simple Harmonic Motion include a constant period (time for one complete oscillation), a constant frequency (number of oscillations per unit time), and a constant amplitude (maximum displacement from equilibrium position). Additionally, the motion is always symmetrical about the equilibrium position.

3)

What is the relationship between Simple Harmonic Motion and Hooke's Law?

Hooke's Law states that the force exerted by a spring is directly proportional to the distance it is stretched or compressed from its equilibrium position. This means that the force acting on an object undergoing Simple Harmonic Motion is directly proportional to its displacement from equilibrium, making Hooke's Law a fundamental principle in understanding SHM.

4)

What are some real-world examples of Simple Harmonic Motion?

Some common real-world examples of Simple Harmonic Motion include the swinging of a pendulum, the motion of a mass-spring system, and the vibration of a guitar string. Other examples include the motion of a car's suspension system, the motion of a diving board, and the motion of a child on a swing.

5)

What factors affect the period of Simple Harmonic Motion?

The period of Simple Harmonic Motion is affected by the mass of the object, the stiffness of the spring, and the amplitude of the motion. The period is longer for objects with larger mass and stiffer springs, and it is independent of the amplitude of the motion.

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