A-LevelPhysicsOscillations9702/31 · May/June 2018 · Q120 Marks

In this experiment, you will investigate the oscillations of a mass.

(a)Set up the apparatus as shown in Fig. 1.1. • Hang mass M from the string loop near the end of the metre rule. • Ensure that the metre rule is pushing up against the rod of clamp A at approximately the 24 cm mark. • The distance between the rod of clamp A and the string attached to the spring is d. Adjust the position of the stand holding the spring so that d is approximately 30 cm. • Adjust the height of the clamps until the rule is horizontal. Ensure that the spring is vertical. • Measure and record d. • The distance between the rod of clamp A and the string supporting M is s. Measure and record s.[1]
(b)• Pull M down through a short distance. • Release M so that it oscillates. • Determine the period T of these oscillations.[1]
(c)• Without moving the stands, slide the rule horizontally through the string loop so that d remains constant but s changes. • Adjust the height of the clamps until the rule is horizontal. Ensure that the spring is vertical. • Measure and record s. • Repeat (b).[1]
(d)Vary s and repeat (c) until you have five sets of values of s and T. You may include your previous sets of readings. Record your results in a table. Include values of T² in your table.[9]
(e)(i)Plot a graph of T² on the y-axis against s on the x-axis.[3]
(e)(ii)Draw the straight line of best fit.[1]
(e)(iii)Determine the gradient and y-intercept of this line.[2]
(f)It is suggested that the quantities T and s are related by the equation T² = Ps + Q where P and Q are constants. Using your answers in (e)(iii), determine the values of P and Q. Give appropriate units.[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 (May/June 2018). The mark or mark type is shown in brackets.

[1] Value of raw d to nearest mm with unit and in the range 29.0–31.0 cm.
[1] Value of T in the range 0.8-2.0s with unit and evidence of at least two sets of nT where n ≥ 5.
[1] Second set of values of s and T.
[4] Five sets of readings of s and time (different values) with the correct trend and without help from the Supervisor scores 4 marks, four sets scores 3 marks etc.
[1] Range: at least one value of s ≤ 70.0 cm and at least one value of s > 85.0 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. s/cm, T/s, T²/s² or T² (s²).
[1] Consistency: All raw time values must be given to 0.1 s or all given to 0.01s.
[1] Significant figures: All values of T² must be given to the same number of s.f. as (or one more than) the number of s.f. in the raw value(s) of time. If raw times are given to 0.01s, allow T² to be recorded to 1 s.f. less than the raw times.
[1] Calculation: Values of T² are correct.
[1] Axes: Sensible scales must be used, no awkward scales (e.g. 3:10 or fractions). 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 that is being plotted. Scale markings should be no more than three large squares apart.
[1] Plotting of points: All observations in the table must be plotted on the grid. Diameter of plotted points must be < half a small square (no "blobs”). Points must be plotted to an accuracy of half a small square.
[1] Quality: All points in the table must be plotted on the grid for this mark to be awarded. It must be possible to draw a straight line that is within ± 2.5 cm (to scale) on the s axis (normally x axis) of all plotted points.
[1] Line of best fit: Judge by balance of all points on the grid about the candidate's line (at least 4 points). There must be an even distribution of points either side of the line along the full length. Allow one anomalous point only if clearly indicated (i.e. circled or labelled) by the candidate. There must be at least four points left after the anomalous point is disregarded. Line must not be kinked or thicker than half a small square.
[1] Gradient: The hypotenuse of the triangle used must be greater than half the length of the drawn line. The method of calculation must be correct. Do not allow Δx/Δy. Both read-offs must be accurate to half a small square in both the x and y directions. Sign of gradient must match graph.
[1] y-intercept: Correct read-off from a point on the line substituted correctly into y = mx + c or an equivalent expression. Read-off must be accurate to half a small square in both x and y directions. or Intercept read directly from the graph, with read-off at s = 0, accurate to half a small square in y direction.
[1] Value of P = candidate's gradient and value of Q = candidate's intercept. The values must not be fractions.
[1] Unit for P correct (e.g. s²m⁻¹ or s²cm⁻¹ or s²mm⁻¹). and Unit for Q is s².