Consider the accelerometer design shown in Figure P4.57, in which a small sphere sits in...

Consider the accelerometer design shown in Figure P4.57, in which a small sphere sits in a hemispherical dish. Suppose the dish has an acceleration of along the horizontal and a small amount of friction causes the sphere to reach a stable position relative to the dish as shown in the figure. Find the position of the sphere (i.e., find the angle ) as a function of