A-LevelPhysicsOscillations9702/32 · May/June 2021 · Q220 Marks

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

(a)(i)Set up the apparatus as shown in [Figure 2.1] using the 50g mass hanger. Pull the mass hanger down by approximately 1cm. Release it so that it oscillates vertically, with no swinging motion. Take measurements to find the period T_V of these oscillations.[2]
(a)(ii)Ensure that the mass hanger has stopped moving. Push the mass hanger approximately 1cm away from you. Release it so that it swings towards and away from you, with as little vertical oscillation as possible. Take measurements to find the period T_S of these oscillations.[1]
(b)Repeat (a) with a total mass of 150g suspended from the spring.[2]
(c)(i)Using your data, calculate two values of T_S² – T_V².[1]
(c)(ii)Justify the number of significant figures you have given for your values of T_S² – T_V².[1]
(c)(iii)Explain whether your results in (c)(i) support the suggestion.[1]
(d)(i)Remove the masses from the spring and the spring from the rod. Measure and record the length x₁ of the spring, as shown in [Figure 2.2].[1]
(d)(ii)Estimate the percentage uncertainty in your value of x₁. Show your working.[1]
(d)(iii)Measure and record the length x₂ of the mass hanger, as shown in [Figure 2.3].[1]
(d)(iv)Using your first value of T_S² – T_V², calculate g using g = 4π²(x₁ + x₂)/(T_S² – T_V²).[1]
(e)(i)Describe four sources of uncertainty or limitations of the procedure for this experiment.[4]
(e)(ii)Describe four improvements that could be made to this experiment. You may suggest the use of other apparatus or different procedures.[4]

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 2021). The mark or mark type is shown in brackets.

[1] Value of T_V with unit and in range 0.20-0.40 s.
[1] At least two measurements of nT_V where n ≥ 5.
[1] Value for T_S larger than T_V.
[1] Second values of T_V and T_S.
[1] Second T_S > first T_S.
[1] Two values of T_S² – T_V² calculated correctly.
[1] Justification based on significant figures in T_S and T_V.
[1] Valid comment consistent with the calculated values of T_S² – T_V², testing against a criterion stated by the candidate.
[1] Value for x₁ in range 4.0–6.0 cm.
[1] Percentage uncertainty based on an absolute uncertainty in the range 2–3 mm. If repeat readings have been taken, then the absolute uncertainty can be half the range (but not zero) if the working is clearly shown. Correct method of calculation to obtain percentage uncertainty.
[1] Raw value(s) for x₂ to nearest 0.1 cm.
[1] Correct calculation of g with consistent unit.
[4] Two T_S² – T_V² values are not enough to draw a (valid) conclusion (not “not enough for accurate results”, “few readings”).
[4] Difficult to maintain single mode of oscillation e.g. spring swings when measuring vertical oscillations/spring bounces when measuring swinging oscillations/spring swings in more than one plane.
[4] Spring slides along rod during the oscillation.
[4] Difficult to judge/determine/decide when an oscillation starts/ends/is complete.
[4] Large % uncertainty in T_V or T_V is small so large uncertainty.
[4] Difficult to measure x₁ or x₂ with reason e.g. parallax error or difficult to measure x₂ due to space at end of ruler. 1 mark for each point up to a maximum of 4.
[4] Take more readings and plot a graph or take more readings and compare (not “repeat readings” on its own).
[4] Method to help maintain single mode of oscillation e.g. restrict sideways motion with tube/use parallel guides.
[4] Method to attach spring to rod/stop spring sliding on rod e.g. adhesive putty/glue spring to rod/cut notch in rod/use rod with diameter same as diameter of spring loop/rougher rod.
[4] Video/record/film with timer in view/frame by frame or use fiducial marker at centre of oscillation.
[4] Use larger masses/use spring with lower spring constant/stiffness.
[4] Use calipers/travelling microscope/use ruler starting at zero/use blocks with detail. 1 mark for each point up to a maximum of 4.