5. A particle of mass m moves in the one-dimensional potential x2 U(x) = U, Se-x/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 → t. Here a is a |constant. Find out the values of potential at local minima and/or maxima point(s). |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) (b) (c)

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.