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.

j' E -k'