Model Pendulum w/ Damping: Newton's Laws & Rubber Band

• bsmith6661
In summary, the conversation discusses modeling a pendulum with damping and a rubber band using Newton's Laws. It is noted that the rubber band acts similarly to a spring but is nonlinear for larger displacements. The equation of motion must take into account the direction of displacement and gravity.
bsmith6661
I feel like this is a dumb question, but here goes: I'm trying to model a pendulum with damping. The pendulum is connected to a rubber band (unstretched when the pendulum is vertical) on the right side, and the rubber band is fixed at the other end. How would I go about modeling a rubber band using Newton's Laws? Everything needs to be in terms of m, k, and c. I know that a rubber band acts similarly to a spring, but can it be modeled as such?

For very small displacements, the rubber band will act approximately like a spring. For larger displacements, you will find that the rubber band is nonlinear. From you description of the system, it sounds like the rubber band will only be taut for displacements to the left. You will need to take that into account when you write the equation of motion. Gravity, of course, will act no matter which direction the pendulum is displaced.

1. What is a model pendulum with damping?

A model pendulum with damping is a physical representation of a pendulum system that includes a damping force, such as air resistance or friction, which causes the pendulum to eventually come to rest. This type of model is used to study the effects of damping on the motion of the pendulum.

2. What are Newton's laws and how do they relate to the model pendulum with damping?

Newton's laws of motion are three fundamental principles that describe the behavior of objects in motion. The first law states that an object will remain at rest or in motion at a constant velocity unless acted upon by an external force. The second law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. The third law states that for every action, there is an equal and opposite reaction. These laws are important in understanding the motion of the pendulum and how the damping force affects it.

3. How does a rubber band affect the motion of the model pendulum with damping?

A rubber band can be used as a source of damping in a model pendulum system. As the pendulum swings back and forth, the rubber band will stretch and exert a force that opposes the motion, causing the pendulum to eventually come to rest. The amount of damping can be adjusted by changing the stiffness of the rubber band.

4. What are the applications of studying a model pendulum with damping?

Studying a model pendulum with damping can have various applications in different fields. In physics, it can help understand the effects of damping on the motion of objects and the application of Newton's laws. In engineering, it can be used to design structures that can withstand external forces, such as wind, that may act as a damping force. In mathematics, it can be used to model and solve differential equations.

5. How can the model pendulum with damping be used to teach about scientific concepts?

The model pendulum with damping can be used as a hands-on tool to demonstrate scientific concepts, such as Newton's laws, damping, and simple harmonic motion. By adjusting the parameters of the model, students can observe how different factors affect the motion of the pendulum and apply their knowledge to real-world situations. It also allows for experimentation and data collection, making it an effective teaching tool for understanding complex scientific concepts.

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