# Show that the period of small oscialltions of the pendulum around its vertical axis

1. Aug 16, 2011

### blueyellow

1. The problem statement, all variables and given/known data

PLEASE DO NOT DELETE THIS POST, MODS, IT MAY LOOK LIKE THE SAME QUESTION AS BEFORE, BUT IT IS NOT, IT IS A TOTALLY DIFFERENT PART TO THE QUESTION.

consider a parallel=plate capacitor with square plates of side L and distance d (<<L) between them, charged with charges +Q and -Q. The plates of the capacitor are horizontal, with the lowest lying on the x-y plane, and the orientation is such that their sides are parallel to the x and y axis, respectively.

a simple pendulum of length d/2 and mass m, hangs vertically from the centre of the top plate, that can oscillate in the x-z plane.

recall that the differential equation for a mechanical simple pendulum in the gravitational field is ml *theta(double primed)=-mg*theta, where theta is the angular displacement from the vertical. Considering the electrical force only, and neglecting gravity, show that the period of small oscillations of the pendulum around its vertical axis is

T=2pi*sqrt[((L^2)*d*m*epsilon0)/(2Qq)]

3. The attempt at a solution

the notes say
omega0=sqrt[(Ze^2)/(4 pi *spsion 0*m(subscript e) *r^3)]

I tried to understand how this related to the question but don't see an obvious connection

2. Aug 19, 2011

### blueyellow

Re: show that the period of small oscialltions of the pendulum around its vertical ax

the mass has charge q, i neglected to say

3. Aug 19, 2011

### Staff: Mentor

Re: show that the period of small oscialltions of the pendulum around its vertical ax

If it's a multiple part question, all parts belong in the same thread.

Hint: Can you derive the period of a pendulum under gravity alone? It's the same problem, only now the force is due to the electric field, not gravity.

4. Aug 19, 2011

### ehild

Re: show that the period of small oscialltions of the pendulum around its vertical ax

No wonder, as it has no connections with your problem. It can be the angular velocity of an electron around a nucleus with Z protons.

Try to solve the problem using your knowledge and logic instead of trying to find a formula with omega at the left-hand side and wondering what to plug in for z and r, when you have q, Q and L.

ehild