(Solved): 6. (3 points) A non-linear spring exerts a restoring force given by \[ F^{\sim}(x)=\left(-k_{1} x- ...

6. (3 points) A non-linear spring exerts a restoring force given by \[ F^{\sim}(x)=\left(-k_{1} x-k_{3} x^{3}\right)^{x} x . \] (a) Show that the force is conservative. (b) Find the potential energy function for this spring. (c) Check your answer for part b) by recovering the force function from the potential energy function.