 Solution

ID: past-exam-of-the-mathematical-methods-i-course-of-the-university-of-oxford/2017-resit/7/a/solution

m \overset{x}{¨} = - k x

, so

ω_{0} = k / m

x (t) = x_{0} cos ω_{0} t, K (t) = \frac{k x _{0}^{2}}{2} sin^{2} ω_{0} t, U (t) = \frac{k x _{0}^{2}}{2} cos^{2} ω_{0} t .

The kinetic energy and elastic potential energy exchange periodically while their sum

E_{0} = k x_{0}^{2} /2

is constant.

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