State the names of the two forces acting on the block while it is at rest.
The block is now pushed down as shown in Fig. 3.2 so that the water surface is higher up the block. State and explain the direction of the resultant force acting on the wooden block in this position.
The block in (b) is now released so that it oscillates vertically. The resultant force $F$ acting on the block is given by $F = -Ag\rho x$, where $g$ is the gravitational field strength and $x$ is the vertical displacement of the block from the equilibrium position. Explain why the oscillations of the block are simple harmonic.
Show that the angular frequency $\omega$ of the oscillations is given by $\omega = \sqrt{\frac{Ag\rho}{m}}$.
The block is now placed in a liquid of greater density. It is displaced and released so that it oscillates vertically. The graph of acceleration $a$ against displacement $x$ for the first half of the oscillation is measured, as shown in Fig. 3.3. Explain why the maximum negative displacement of the block is not the same as its maximum positive displacement.
The mass of the block is $0.57\,\text{kg}$. Use Fig. 3.3 to calculate the decrease $\Delta E$ in the energy of the oscillation during the first half oscillation.