# Possible motion of a concial pendulum?

Suppose we have a "conical pendulum" consisting of a bob $P$ of mass $m$ attached to a rigid chord of length $l$ which is attached at its other end to a fixed point $O$. We displace the bob so that it forms an angle $\theta_0$ with the vertical axis and give it some initial velocity $\vec{v_0}$.

What are the possible motions of the pendulum?

We can first consider the easy case where $\vec{v_0}$ is horizontal.

Note: "conical pendulum" just means a pendulum which is allows to move in 3 dimmensions as opposed to the classic planar pendulum motion

• ? conical $\hspace{10mm}$ May 7, 2017 at 15:58

• Angular momentum is conserved. Is there an easy way to see this, because I just proved it by expressing the acceleration in cylindrical coordinates and noting that there is no component of force in the $\vec{e_\theta}$ direction. Also could you please elaborate on what you said, at least flesch out the main ideas a bit because I don't understand why we would get oscillator equations. I found two coupled equations (for $z$ and for $r$), they both depend on the tension in the chord. May 7, 2017 at 16:34