Nonlinear graph in the Physical Pendulum

In summary, an experiment using a physical pendulum to measure gravitational acceleration g was conducted. A graph was shown, indicating a nonlinear trend despite assuming small-amplitude oscillations. This trend was observed as the pivot point moved closer to the centroid, which contradicts the equation found in the provided link. It is speculated that this could be due to the presence of a damping force, where a decrease in d causes the small-amplitude oscillations to become larger, resulting in a non-linear graph.
  • #1
omicgavp
13
0
We did an experiment using the physical pendulum to measure gravitational acceleration g. A graph is shown in this link:
http://i593.photobucket.com/albums/tt20/omicgavp/measuringggraph.jpg"

A nonlinear (possibly chaotic) trend can be seen in our graph even though we assumed small-amplitude oscillations. This trend has been observed as the pivot point goes near to the centroid. How did this happen? It disagrees with our equation (theory) found in the link! Can this be due to the damping force?
 
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  • #2
T=period, I=moment of inertia, M=mass of the system, g=gravitational acceleration, d=distance from pivot point to centroid
 
  • #3
I guess when d decreases, the otherwise small-amplitude oscillations become not so small, and that is why the graph is no longer linear.
 

FAQ: Nonlinear graph in the Physical Pendulum

1. What is a physical pendulum?

A physical pendulum is a real-life example of a simple pendulum, which is a mass attached to a rigid, weightless arm that is free to swing back and forth. In a physical pendulum, the mass is not concentrated at a single point, but is instead spread out along the arm. This creates a more complex and nonlinear motion compared to a simple pendulum.

2. How do you represent a nonlinear graph in a physical pendulum?

A nonlinear graph in a physical pendulum is typically represented by plotting the angle of rotation (theta) against time. The resulting graph will not form a straight line, but rather a curve that oscillates back and forth. The shape of this curve depends on the length and mass distribution of the pendulum, as well as the initial conditions of the swing.

3. What factors affect the motion of a physical pendulum?

The motion of a physical pendulum is affected by several factors, including the length of the pendulum arm, the mass distribution along the arm, the initial angle of release, and the presence of external forces such as friction or air resistance. The shape of the pendulum also plays a role, as different shapes can create different moments of inertia that affect the motion.

4. How is the period of a physical pendulum calculated?

The period of a physical pendulum is calculated using the equation T = 2π√(I/mgd), where T is the period, I is the moment of inertia, m is the mass of the pendulum, g is the acceleration due to gravity, and d is the distance from the pivot point to the center of mass. This equation takes into account the nonlinear motion of the pendulum and provides a more accurate estimate of the period compared to the simple pendulum equation.

5. What real-world applications use the concept of a physical pendulum?

Physical pendulums have various real-world applications, such as in clocks, seismometers, and accelerometers. They are also used in research and analysis of complex systems, as their nonlinear motion can provide insights into chaotic behavior. In addition, physical pendulums are commonly used in physics demonstrations and experiments to illustrate principles such as rotational motion and oscillations.

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