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## Homework Statement

A harmonic potential is parameterised as:

[tex]V(x)=\frac{k}{2}(x-x_{0})^2[/tex]

An object moves within this potential with a total energy E > 0.

(i) Where are the two turning points of the motion xA and xB?

(ii) Write down the equation of motion for the object, and use it to find explicit expressions for the kinetic and potential energies as a function of time. Show that the total energy is constant.

(iii) Show that the period of oscillation is given by:

[tex]t= \sqrt{2m}\int_{X_{a}}^{X_{b}}\frac{dx}{\sqrt{E-V(x)}}[/tex]

and evaluate this integral for the given potential.

## Homework Equations

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OK so I have worked my way through part (i) and (ii) , but I can not see how that integral is the right one, surely this is just integrating 2/v wrt x? I don't understand how that would get you the period?

## The Attempt at a Solution

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