Practise identifying SHM from acceleration proportional to opposite displacement, locating the fixed point and explaining restoring conditions.
A small wooden block (cuboid) of mass m floats in water, as shown in Fig. 3.1.
Fig. 3.1
The top face of the block is horizontal and has area A. The density of the water is .
The block in (b) is now released so that it oscillates vertically.
The resultant force F acting on the block is given by
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.