Answer to Question #169584 in Classical Mechanics for Rohan

Question

Consider a particle moving in a central force field

           f(u) = - ku²

using standard notation u =1/r. The quantity 

d²u/dθ² + u

(a) is proportional to u²

(b) is proportional to u

(c) is a constant

(d) is proportional to 1/u

(e) none of these

Answer 1

$$\frac{d^2u}{d\theta^2}+u=-\frac{f(u)}{mh^2u^2}\\ \frac{d^2u}{d\theta^2}+u=-\frac{ - ku^2}{mh^2u^2} \\ \frac{d^2u}{d\theta^2}+u=\frac{ k}{mh^2}=const$$

Answer: (c) is a constant