A U-shaped tube contains some liquid. The liquid column in each half of the tube has length L, as shown in [Figure 3.1]. The liquid columns are displaced vertically. The liquid then oscillates in the tube. The liquid levels are displaced from the equilibrium positions as shown in [Figure 3.2]. The acceleration a of the liquid in the tube is related to the displacement x by the expression a = -(g/L)x where g is the acceleration of free fall.

1. (a)Explain how the expression shows that the liquid in the tube is undergoing simple harmonic motion.[3]
2. (b)The length L of each liquid column is 18 cm. Determine the period T of the oscillations.[3]
3. (c)The oscillations of the liquid in the tube are damped. In any one complete cycle of the oscillations, the amplitude decreases by 6.0% of its value at the beginning of the oscillation. Determine the ratio energy of oscillations after 3 cycles / initial energy of oscillations[3]

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