Motion in a Force Field A mathematical model for the
Chapter 4, Problem 23E(choose chapter or problem)
Motion in a Force Field A mathematical model for the position x(t) of a body moving rectilinearly on the x-axis in an inverse-square force field is given b
\(\frac{d^{2} x}{d t^{2}}=-\frac{k^{2}}{x^{2}}\)
Suppose that at \(t=0\) the body starts from rest from the position \(x=x_{0}, \quad x_{0}>0\). Show that the velocity of the body at time t is given by \(v^{2}=2 k^{2}\left(1 / x-1 / x_{0}\right)\). Use the last expression and a CAS to carry out the integration to express time t in terms of x.
Text Transcription:
fracd^2xdt^2=-frack^2x^2
t=0
x=x_0,x_0>0
v^2=2k^21/x-1/x_0
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