A particle of mass m moves in the one-dimensional potential U(x) = U, (a) Sketch U(x). Identify the location(s) of any local minima and/or maxima, and |be sure that your sketch shows the proper behaviour as x → t0. Here a is a constant. (b) Find out the values of potential at local minima and/or maxima point(s). (c) Sketch the phase portrait corresponding to the potential obtained in part (a). (d) Derive the expression for the time period of the motion when |x| « a.
A particle of mass m moves in the one-dimensional potential U(x) = U, (a) Sketch U(x). Identify the location(s) of any local minima and/or maxima, and |be sure that your sketch shows the proper behaviour as x → t0. Here a is a constant. (b) Find out the values of potential at local minima and/or maxima point(s). (c) Sketch the phase portrait corresponding to the potential obtained in part (a). (d) Derive the expression for the time period of the motion when |x| « a.
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Transcribed Image Text:5.
A particle of mass m moves in the one-dimensional potential
U (x) = U,
(a)
Sketch U(x). Identify the location(s) of any local minima and/or maxima, and
be sure that your sketch shows the proper behaviour as x → ±. Here a is a
constant.
(b)
Find out the values of potential at local minima and/or maxima point(s).
(c)
Sketch the phase portrait corresponding to the potential obtained in part (a).
(d)
Derive the expression for the time period of the motion when |x| « a.
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