Considering the Earth as an inertial frame of reference, we can apply Newton’s second law to the pendulum: + = m, with the weight of the pendulum and m its mass, the tension in rod, and the centripetal acceleration (see Fig. 1).
We thus deduce :
and consequently
| (3) |
If we consider l sin θ as negligible compared to R, we get the 0th-order solution:
| (4) |