A hollow tube, sealed at one end, has a cross-sectional area A of 24 cm². The tube contains sand so that the total mass M of the tube and sand is 0.23 kg. The tube floats upright in a liquid of density ρ, as illustrated in Fig. 3.1. [Figure 3.1] The depth of the bottom of the tube below the liquid surface is h. The tube is displaced vertically and then released. The variation with time t of the depth h is shown in Fig. 3.2. [Figure 3.2]

1. (a)(i)Determine: the amplitude, in metres, of the oscillations[1]
2. (a)(ii)the frequency of oscillation of the tube in the liquid[2]
3. (a)(iii)the acceleration of the tube when h is a maximum.[2]
4. (b)The frequency f of oscillation of the tube is given by the expression f = 1/(2π) √((Aρg)/M) where g is the acceleration of free fall. Calculate the density ρ of the liquid in which the tube is floating.[2]
5. (c)The oscillations illustrated in Fig. 3.2 are undamped. In practice, the liquid does cause light damping. On Fig. 3.2, draw a line to show light damping of the oscillations for time t = 0 to time t = 1.4s.[3]

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