Find the damping constant of the Pendulum

In summary, the conversation discusses a physical pendulum with specific dimensions and mass, undergoing oscillations with reduced amplitude due to friction. The question is how to find the damping constant b, with the given values for moment of inertia and center of mass. The equation I=mr^2/2 is mentioned but the person is unsure where to begin.
  • #1
darkspy123
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0

Homework Statement


A physical pendulum consists of a uniform sphere with radius r=2.5cm and mass M = 0.5kg attached to a uniform rod with length L = 1m and mass m=250g

The friction of the suspension and air moderately reduce the amplitude of oscillation by factor of 2 in 19.6s. What is the damping constant b? Let's assume that the period of oscillation does not change during this time.

I found the moment of inertia to be 0.609 and the center of mass from the pivot point is 0.85m. I'm stuck here
 
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  • #2
, I'm not sure how to find the damping constant b.Homework Equations I=mr^2/2The Attempt at a SolutionI'm not sure where to start.
 

1. How does a pendulum work?

A pendulum works by converting potential energy into kinetic energy and back again. When the pendulum is at the highest point, it has the most potential energy. As it swings down, the potential energy is converted into kinetic energy. As it reaches the bottom, the kinetic energy is at its maximum and the pendulum begins to swing back up, converting the kinetic energy back into potential energy.

2. What factors affect the motion of a pendulum?

The motion of a pendulum can be affected by several factors, including the length of the pendulum, the weight of the pendulum bob, and the amplitude of the swing. Other factors such as air resistance, friction, and temperature can also impact the motion of a pendulum.

3. How is the damping constant of a pendulum calculated?

The damping constant of a pendulum can be calculated by measuring the amplitude of the pendulum's swing over time and using the equation θ = θ0e^(-bt/2m) where θ is the amplitude, θ0 is the initial amplitude, b is the damping constant, t is time, and m is the mass of the pendulum bob.

4. What is the significance of the damping constant in a pendulum?

The damping constant in a pendulum represents the rate at which the pendulum's motion decreases due to external factors such as air resistance and friction. A higher damping constant means the pendulum will lose its energy and come to a stop more quickly, while a lower damping constant means the pendulum will continue to swing for a longer period of time.

5. Can the damping constant of a pendulum be changed?

Yes, the damping constant of a pendulum can be changed by altering external factors such as the length of the pendulum, the weight of the pendulum bob, or the amplitude of the swing. It can also be changed by changing the material or shape of the pendulum bob, which can affect air resistance and friction. Additionally, the damping constant can be influenced by the environment, such as temperature and air density.

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