A-LevelPhysicsOscillations9702/33 · Feb/Mar 2020 · Q120 Marks

In this experiment you will investigate the oscillations of a rod.

(a)The distance between the two springs where they support the rod is x, as shown in Fig. 1.1. Measure and record x. x = .............................................. cm[1]
(b)Lift one end of the rod a short distance and push the other end of the rod down a short distance. Release the rod so that it oscillates with a rocking motion, as shown in Fig. 1.2. Take measurements to determine the period T of the oscillation. T = .............................................. s[2]
(c)Change x by moving the stands. Adjust the apparatus until the springs are vertical and the rod is parallel to the bench. Measure x and T. Repeat until you have six sets of values of x and T. Record your results in a table. Include values of 1/x in your table.[9]
(d)(i)Plot a graph of T on the y-axis against 1/x on the x-axis.[3]
(d)(ii)Draw the straight line of best fit.[1]
(d)(iii)Determine the gradient and y-intercept of this line. gradient = ................................................................ y-intercept = ................................................................[2]
(e)It is suggested that the quantities T and x are related by the equation T = a/x + b where a and b are constants. Use your answers in (d)(iii) to determine the values of a and b. Give appropriate units. a = ................................................................ b = ................................................................[2]

This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.

Mark scheme

Marking points from the official mark scheme (Feb/Mar 2020). The mark or mark type is shown in brackets.

[1] Value of x in range 10.0 to 20.0 cm
[1] Value of T in range 0.50 to 1.50 s
[1] Evidence of repeat readings: at least two values of at least 5T
[4] Six sets of readings of x and T with correct trend and without help scores 4 marks, five sets scores 3 marks etc.
[1] Range: Xmin < 12.0 cm and Xmax > 25.0 cm
[1] Column headings: Each column heading must contain a quantity and a unit where appropriate. The presentation of quantity and unit must conform to accepted scientific convention e.g. 1 / x (cm⁻¹)
[1] Consistency: All values of raw x must be given to the nearest mm
[1] Significant figures: All values of 1 / x should be to the same s.f. as (or one more than) the s.f. in the corresponding x value
[1] Calculation: Values of 1/x calculated correctly
[1] Axes: Sensible scales must be used, no awkward scales (e.g. 3:10). Scales must be chosen so that the plotted points occupy at least half the graph grid in both x and y directions. Scales must be labelled with the quantity which is being plotted. Scale markings should be no more than 3 large squares apart.
[1] Plotting of points: All observations must be plotted on the grid. Diameter of plotted points must be < half a small square (no blobs). Plots must be accurate to within half a small square in both x and y directions.
[1] Quality: All points in the table must be plotted (at least 5) for this mark to be awarded. Scatter of plots must be no more than ± 0.5 m⁻¹ (± 0.005 cm⁻¹) from a straight line in the x-direction.
[1] Line of best fit: Judged by balance of all points on the grid (at least 5) about the candidate's line. There must be an even distribution of points either side of the line along the full length. One anomalous point is allowed only if clearly indicated (i.e. circled or labelled) by the candidate. Lines must not be kinked or thicker than half a square.
[1] Gradient: The hypotenuse of the triangle used must be greater than half the length of the drawn line. Method of calculation must be correct. Both read-offs must be accurate to half a small square in both the x and y directions.
[1] y-intercept: Either Correct read-off from a point on the line substituted into y = mx + c or an equivalent expression, with read-off accurate to half a small square in both x and y directions. Or Intercept read directly from the graph, with read-off at x = zero accurate to half a small square in y direction.
[1] a equal to candidate's gradient, and b equal to candidate's intercept. a and b are not fractions. a has two or more significant figures.
[1] Units for a and b correct (e.g. s cm or s m for a, and s for b).