Check your results in Problem 1.11(b) with the following “numerical experiment.” The position of the oscillator at time t is x(t) = A cos(ωt).

You might as well take ω = 1 (that sets the scale for time) and A = 1 (that sets the scale for length). Make a plot of x at 10,000 random times, and compare it with ρ(x).
In Mathematica, first define

then construct a table of positions:

and finally, make a histogram of the data:

Meanwhile, make a plot of the density function, ρ(x), and, using Show, superimpose the two.

Problem 1.11(b)

(b) Determine Δj for each j, and use Equation 1.11 to compute the standard deviation.

Equation 1.11

Transcribed Image Text:

x[t_] := Cos[t]