A long wooden cylinder floats vertically in a liquid. The length of the cylinder below the liquid level is 20 cm20\text{ cm}20 cm.
The pressure exerted by the liquid alone on the bottom of the cylinder is 1.8×103 Pa1.8 \times 10^3\text{ Pa}1.8×103 Pa. Calculate the density ρ\rhoρ of the liquid to 2 significant figures. (Use g=9.81 m s−2g = 9.81\text{ m s}^{-2}g=9.81 m s−2)
The cylinder is pushed down into the liquid and then released so that it oscillates freely with simple harmonic motion at a frequency of 1.2 Hz1.2\text{ Hz}1.2 Hz. At t=0 st = 0\text{ s}t=0 s, the cylinder is released from its maximum displacement of 3.0 cm3.0\text{ cm}3.0 cm.
Calculate the displacement xxx (in cm\text{cm}cm) of the cylinder at time t=0.50 st = 0.50\text{ s}t=0.50 s.
Calculate the maximum speed of the oscillating cylinder (in m s−1\text{m s}^{-1}m s−1) to 2 significant figures.
State the effect of pushing the cylinder down further before release on its (1) amplitude and (2) period.
