Physics 9702 · AS & A Level · Damped and forced oscillations, resonance
Damped and forced oscillations, resonance — practice question
A U-tube is shown in Fig. 3.1 containing a liquid. The full length of the liquid column in the tube is $L$. The column is then shifted so that the rise or fall of the liquid in each arm of the U-tube is $x$, as shown in Fig. 3.2. The liquid in the U-tube then carries out simple harmonic motion, with the column acceleration $a$ given by $a = -\left(\frac{2g}{L}\right)x$, where $g$ is the acceleration of free fall.
(a)[3]
Calculate the period $T$ of oscillation of the liquid column when the column length is $19.0\,\text{cm}$.
(b(i))[1]
Suggest one cause of the damping.
(b(ii))[3]
Calculate the loss in total energy of the oscillations in the first $2.5$ periods of the oscillations.
Worked solution & mark scheme
This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “$\omega^2 = \frac{2g}{L}$” …