A dish is made from a section of a hollow glass sphere. The dish, fixed to a horizontal table, contains a small solid ball of mass 45g, as shown in Fig. 4.1. The horizontal displacement of the ball from the centre C of the dish is x. Initially, the ball is held at rest with distance x = 3.0 cm. The ball is then released. The variation with time t of the horizontal displacement x of the ball from point C is shown in Fig. 4.2. The motion of the ball in the dish is simple harmonic with its acceleration a given by the expression a = -(g/R)x where g is the acceleration of free fall and R is a constant that depends on the dimensions of the dish and the ball. [Figure 4.1] [Figure 4.2]

1. (a)Use Fig. 4.2 to show that the angular frequency ω of oscillation of the ball in the dish is 2.9 rad s⁻¹.[1]
2. (b)(i)Use the information in (a) to: determine R[2]
3. (b)(ii)calculate the speed of the ball as it passes over the centre C of the dish.[2]
4. (c)Some moisture collects on the surface of the dish so that the motion of the ball becomes lightly damped. On the axes of Fig. 4.2, draw a line to show the lightly damped motion of the ball for the first 5.0s after the release of the ball.[3]

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