A-LevelPhysicsOscillations9702/31 · Oct/Nov 2021 · Q120 Marks

In this experiment, you will investigate oscillations.

(a)• Slide the loop of a spring onto a wooden rod. Fix the loop of a spring in the middle of the wooden rod with a clip, as shown in Fig. 1.1. [Figure 1.1] • Use half of the adhesive putty to fix four 10g masses to the wooden rod as shown in Fig. 1.2. [Figure 1.2] • Adjust the positions of the masses until the distance between the masses is approximately 22 cm. The masses should each be approximately the same distance from the clip, as shown in Fig. 1.2. • Clamp the loop at the top of the spring between two small wooden blocks. • Arrange the apparatus as shown in Fig. 1.3. [Figure 1.3] • Adjust the position of the clip until the rod balances approximately parallel to the bench. • The distance between the masses on the wooden rod is x, as shown in Fig. 1.3. Measure and record x.[1]
(b)• Using the other wooden rod, set up a second set of apparatus as shown in Fig. 1.3. • The distance between the masses on this wooden rod is p. Adjust the position of the masses until the value of p is approximately 18 cm. • Measure and record p.[1]
(c)• Move the apparatus until the two rods are close to each other and in line as shown in Fig. 1.4. [Figure 1.4] • Gently press the rods down at end X and end P. • Release the ends at the same time. The ends will oscillate as shown in Fig. 1.5. [Figure 1.5] • Watch the oscillations. X and P move in and out of phase. • Look at P. Count the number n of oscillations made by P from release until both ends are back in phase.[1]
(d)Change p in the range 14.0 cm < p < 20.5 cm and repeat (c) until you have six sets of values of p and n. Keep distance x constant. Record your results in a table. Include values of 1/p and 1/n in your table. Record the values of 1/n to three significant figures.[9]
(e)(i)Plot a graph of 1/n on the y-axis against 1/p 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 n and p are related by the equation 1/n = A/p + B where A and B are constants. Using your answers in (e)(iii), determine the values of A and B. 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 (Oct/Nov 2021). The mark or mark type is shown in brackets.

[1] (a) Value of x with unit and in the range 21.0–23.0 cm.
[1] (b) Value(s) of p to nearest mm and final value with unit and in the range 17.0–19.0 cm.
[1] (c) Value of n with evidence of repeats.
[4] (d) Six sets of readings of p (different values) and n with correct trend and without help from Supervisor scores 4 marks, five sets scores 3 marks etc.
[1] (d) Range: pmin < 15.0 cm and pmax ≥ 19.0 cm.
[1] (d) 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. p/ cm, (1 / p) / (1 / m) or p⁻¹/mm⁻¹. There must be no unit for n or 1/n.
[1] (d) Consistency: All values of p must be given to the nearest mm.
[1] (d) Significant figures: All values of 1/p must be given to the same number of s.f. as, or one greater than, the number of s.f. of the p values as recorded in the table.
[1] (d) Calculation: Values of 1 / p are correct.
[1] (e)(i) 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 the x and y directions. Axes must be labelled with the quantity that is being plotted. Scale markings should be no more than three large squares apart.
[1] (e)(i) Plotting of points: All observations in the table must be plotted on the grid. Diameter of plotted points must be < half a small square. Points must be plotted to an accuracy of half a small square in both x and y directions.
[1] (e)(i) Quality: All points in the table (at least 5) must be plotted on the grid. Trend of points must be correct. It must be possible to draw a straight line that is within ± 0.002 cm¯¹ on the 1/p axis of all plotted points.
[1] (e)(ii) Line of best fit: Judge by the balance of all points on the grid about the candidate's line (at least 5 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 five points left after the anomalous point is disregarded. Line must not be kinked or thicker than half a small square.
[1] (e)(iii) Gradient: The hypotenuse of the triangle used must be greater than half the length of the drawn line. Both read-offs must be accurate to half a small square in both the x and y directions. Method of calculation must be correct, e.g. Δy/Δx. Gradient sign on answer line matches graph drawn.
[1] (e)(iii) y-intercept: Correct read-off from a point on the line and substituted into y = mx + c or an equivalent expression. 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 1 / p = 0, accurate to half a small square.
[1] (f) Value of A = candidate's gradient and value of B = candidate's intercept. Values must not be written as fractions.
[1] (f) Unit for A correct e.g. cm, m or mm and no unit given for B.