# A pendulum in a local reference frame (see Fig. 5.7) is constrained in a point along the

## Question:

A pendulum in a local reference frame (see Fig. 5.7) is constrained in a point along the $$z^{\prime}$$ axis so that it can swing freely in the $$x^{\prime} y^{\prime}$$ plane. The pendulum is geographically located in a city of latitude $$\lambda$$ in the Earth's northern hemisphere. Initially, the pendulum is deflected towards East from its equilibrium position and is allowed to oscillate to the West starting from rest, moving initially along $$\hat{\mathbf{j}}^{\prime}$$. Because of Coriolis acceleration, the pendulum is deflected to the right (i.e., toward the North, direction $$+\hat{\mathbf{i}}^{\prime}$$ ). Determine the value of the angle by which the plane of oscillation rotates every hour, continuously deflecting slightly to the right. Also determine the time required for a complete $$360^{\circ}$$ rotation of the oscillation plane at the latitude of Paris ( $$48^{\circ} 51^{\prime}$$ ) where the experiment was first carried out in 1851 . The pendulum was $$67 \mathrm{~m}$$ long and hung in the dome of the Pantheon.

Fantastic news! We've Found the answer you've been seeking!