Explore BrainMass
Share

# Position probability distribution for a pendulum

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

Position probability distribution for a pendulum. Consider the classical motion of a pendulum bob which, for small amplitudes of oscillation, moves effectively as a harmonic oscillator along a horizontal axis according to the equation.

x(t) = Asinwt

The probability that the bob will be found within a small distance delta x at x in random observations is proportional to the time it spends in this region during each swing. Obtain a mathematical expression for this probability as a function of x, assuming delta x<<A.

© BrainMass Inc. brainmass.com March 22, 2019, 1:23 am ad1c9bdddf
https://brainmass.com/physics/equilibrium/position-probability-distribution-pendulum-536415

#### Solution Preview

We are given a classical pendulum with small amplitude, which moves effectively as a harmonic oscillator along a horizontal axis according to the equation:

x(t) = Asinwt

...............................................................................

** Please see the attached file for the complete solution **

We are ...

#### Solution Summary

We derive the position probability distribution of a classical pendulum (harmonic oscillator) undergoing small oscillations about equilibrium.

\$2.19