A-LevelPhysicsOscillations9702/32 · May/June 2020 · Q120 Marks

In this experiment, you will investigate a pendulum made from a wooden strip with masses fixed at one end.

(a)Some of the apparatus has been assembled for you. • Pass the nail through the hole in the strip furthest from the masses. • Fix the nail securely in the clamp. • Complete the set-up of the apparatus as shown in Fig. 1.1. • The hooks at the ends of the springs should pass through one of the holes in the strip. • Position the stands so that the coiled section of each spring is of approximate length 6 cm and the strip is vertical. The distance along the strip between the nail and the hole with the hooks is d. Measure and record d.[1]
(b)• Move the bottom of the strip towards one of the stands and release it so that it oscillates. • Take measurements to determine the period T of these oscillations.[2]
(c)Move the hooks to a different hole in the strip. Measure d and T. Repeat until you have six sets of values of d and T. Record your results in a table. Include values of d² and 1/T² in your table.[9]
(d)(i)Plot a graph of 1/T² on the y-axis against d² 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.[2]
(e)It is suggested that the quantities T and d are related by the equation 1/T² = ad² + b where a and b are constants. Use your answers in (d)(iii) to 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 (May/June 2020). The mark or mark type is shown in brackets.

[1] Value of d in range 5–40 cm.
[1] Value of T in range 0.10-1.50 s.
[1] Evidence of repeat readings: at least two values of at least 5T.
[4] Six sets of readings of d and T showing the correct trend and without help from the Supervisor scores 4 marks, five sets scores 3 marks etc.
[1] Range: Xmin < 10.0 cm and Xmax > 30.0 cm.
[1] Column headings: Each column heading must contain a quantity, a unit and a separating mark where appropriate. The presentation of the quantity and unit must conform to accepted scientific convention e.g. 1 / T² (s-²).
[1] Consistency: All raw values of d must be given to the nearest mm.
[1] Significant figures: Number of significant figures for every value of d² the same as, or one more than, the number of s.f. in the corresponding value of d.
[1] Calculation: Values of d² 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 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. Points must be plotted to an accuracy of half a small square.
[1] Quality: All points in the table (at least 5) must be plotted on the grid. Trend of points on the graph must be correct. It must be possible to draw a straight line that is within ± 0.20 s¯² on the 1 / T² 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 5 points). There must be an even distribution of points either side of the line along the full length. If there are 6 or more points, allow one anomalous point only if clearly indicated by the candidate. 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 Ax/Ay. Both read-offs must be accurate to half a small square in both the x and y directions.
[1] y-intercept: Correct read-off from a point on the line and substituted into y = mx + c. 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 x = 0 accurate to half a small square.
[1] Value of a equal to candidate's gradient and value of b equal to candidate's intercept. The values must not be fractions.
[1] Units for a (e.g. s-² cm-²) and b (s-²) correct.