Physics 9702 · AS & A Level · Damped and forced oscillations, resonance
Damped and forced oscillations, resonance — practice question
As illustrated in Fig. 3.1, a U-tube holds liquid. The overall length of the liquid column in the tube is $L$. The column is then shifted so that the liquid level in each limb of the U-tube changes by $x$, as shown in Fig. 3.2. The liquid in the U-tube then carries out simple harmonic motion with 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 $L$ is $19.0\,\text{cm}$.
(b(i))[1]
Suggest one reason for the damping.
(b(ii))[3]
Calculate the loss in the total energy of the oscillations over 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: “$\omega^2 = \dfrac{2g}{L}$” …