Probability Density Function for a Pendulum?

Thread starter bencmier
Start date Oct 2, 2012
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Density Density function Function Pendulum Probability Probability density Probability density function

In summary, a probability density function (PDF) is a mathematical function used to represent the probability distribution of a continuous random variable. The PDF for a pendulum is used to describe the probability of the pendulum being at a particular angle at a given time, taking into account factors such as length, mass, initial angle, and external forces. It differs from a simple harmonic oscillator in that it considers gravity and initial conditions, and is important for understanding and predicting the behavior of a pendulum over time. Additionally, it can be used to compare different pendulum systems and make predictions about their motion.

Oct 2, 2012

bencmier

What is the probability density equation as a function of angle for a simple pendulum using the small angle approximation?

I got 1/(2 pi θmax) sec(sqrt(g/L)t) but it doesn't seem right.

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Oct 2, 2012

HallsofIvy

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The probability density of what random variable?

Oct 2, 2012

bencmier

HallsofIvy said:

The probability density of what random variable?

"as a function of angle"

Related to Probability Density Function for a Pendulum?

1. What is a probability density function (PDF)?

A probability density function (PDF) is a mathematical function that describes the relative likelihood of a continuous random variable taking on a particular value. It is used to represent the probability distribution of a random variable.

2. How is the PDF used to describe a pendulum's motion?

The PDF for a pendulum is used to describe the probability of the pendulum being at a particular angle at a given time. It shows how likely it is for the pendulum to be at a certain angle as it swings back and forth.

3. What factors affect the PDF for a pendulum?

The PDF for a pendulum is affected by several factors, including the length of the pendulum, the mass of the pendulum, the initial angle at which it is released, and any external forces acting on the pendulum such as friction or air resistance.

4. How is the PDF for a pendulum different from a simple harmonic oscillator?

The PDF for a pendulum takes into account the effects of gravity and the pendulum's initial conditions, while the PDF for a simple harmonic oscillator does not. This means that the PDF for a pendulum will have a different shape and will change over time as the pendulum swings, while the PDF for a simple harmonic oscillator remains constant.

5. Why is the PDF for a pendulum important?

The PDF for a pendulum is important because it allows us to understand and predict the behavior of a pendulum over time. It can also be used to calculate important quantities such as the average angle or the maximum angle that the pendulum will reach. Additionally, the PDF can be used to compare different pendulum systems and make predictions about their motion.