## Section 6.3: Exploring Classical Probability Distributions

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The relative probability distribution, *P*_{R}(*x*), is shown. For bound systems, where a particle will always be in a certain finite region of space, this distribution can be normalized to yield a normalized probability distribution, *P*_{N}(*x*). Restart.

- Calculate the relative probability distribution,
*P*_{R}(*x*), for a 1-kg particle initially at rest and attached to a spring (a harmonic oscillator) of spring constant*k*= 2 N/m and an initial displacement from equilibrium of 1 m. - Now enter in this function into the text box and set the proper classical limits by clicking the "change limits and evaluate" button. What is the normalized classical probability distribution,
*P*_{N}(*x*)? You must normalize (a) by doing the integral.

Repeat (a) and (b) for a 0.1-kg particle dropped from rest 1 m above the ground. Assume an elastic collision with the ground at *y* = 0 m.

Once you have completed your calculations, check your results using the animations provided below.

particle on a spring | bouncing particle

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