1. Aim To find the relationship between the length of a pendulum and its period of oscillation Equipment String, pendulum bob, stop watch, retort stand, clamp arm and boss head, ruler, cork tiles. Task Set up the equipment: Make sure the clamp stand and clamp arm are firmly fixed and that there is no wobble. Attach the cork tiles to the clamp arm. Carry out the experiment: The period of oscillation is the time it takes to do one complete swing. (This time does not change as the amplitude of the swings changes and so timing multiple bounces is an option.) The amplitude of the oscillations must be kept small (<10 o )

2. Method: identify the dependent and independent variables. Length is the independent variable (A) Time is the dependent variable (A) identify any variables that must be controlled. Release of pendulum should be about 10 0 (M) identify how you maximized the accuracy of the data you gathered. improves accuracy by timing multiple periods and / or by repeating and averaging at least 3 time values for each length. (M)

3. give all raw measurements in an appropriately headed results table, using appropriate units and significant figures. (You must make sufficient measurements to allow you to draw a graph that will help you determine the required relationship.) uses at least 5 values of length over a range of 0.1m to 1.0m. Values are given with a unit. (A) measures a period for each length. Values given with a unit.(A)

4. Data analysis: Plot an appropriate graph to find the type of relationship between period, T and length, l. Draw a curve of best fit (the raw data will not give a straight-line graph). plots measured values on a graph; axes labelled with quantities and units; graph line an appropriate curve.(A) Determine the type of relationship that this graph suggests. states the relationship between is a square root relationship (graph is T against √l) / square relationship (graph is l against T 2 ). (A)

5. Process the data so that you can draw a straight- line graph. Plot and draw the straight-line graph. transforms values of T by squaring / l by square rooting. Transformed values have appropriate significant figures and units.(M) plots appropriate variables to give a linear graph; chooses a scale that allows a gradient with reasonable sf to be found; labels axes with quantities and units; draws a straight graph line that is an appropriate fit to the plotted points.(M) calculates the gradient of the linear graph using a correct method. (Gradient value should be about 4.0±0.5 s 2 m -1 or 2.0±0.5 s m -1/2 )(M)

6. Conclusion: Using information from the straight- line graph, state the mathematical relationship between period, T, and length, l. states the mathematical equation is y- axis variable = gradient of graph line  x-axis variable. (Ignore any intercept the graph line might have.)(M)

7. Discussion: Discussion statements should attempt to validate your conclusion. They could include: How the findings of your investigation relate to stated physics theory. If an unexpected result is obtained you should suggest how it could have been caused or explain the effect it had on the validity of the conclusion.

8. Additional information Physics theory states that, for a pendulum of length l, the period, T is given by: l = g T 2 4 π 2 Where g is the acceleration due to gravity (g = 9.8 m s -2 )

10. For the variables you controlled, a description of how each was controlled and an explanation of why it needed to be controlled. states or implies control of the amplitude by always releasing with an angle of 10 o or less. Larger angles mean the pendulum is travelling faster and can cause sideways motion making it harder to time(M) For the accuracy improving techniques you used, a description of what you did and an explanation of why it needed to be done Justifies the use of repeating and averaging by explaining that each time measurement is subject to a random reaction time error. (M)

11. A description of any difficulties you encountered when making measurements and an explanation of how these difficulties were overcome. Justifies the use of timing multiples by explaining that the time for one period is so short that the human error (random uncertainty) when starting and stopping the stopwatch is significantly large in comparison with the measured time/timing ten swings allows an accuracy to a greater number of significant figures.(E)

12. A reason why there was a limit to the range of values you chose for the independent variable. Justifies their choice of upper value for the length by explaining the limitations of the equipment or height limitation available/time constraints due to the increased period for longer lengths/pendulum swinging off line more with longer lengths.(E) Justifies their choice of lower value for the length by explaining the difficulty of counting the swings as short lengths gave such a short period/inaccuracy due to difficulty measuring the length being more significant with shorter lengths.(E)

13. compares the theoretical gradient with the experimental gradient/calculates an experimental value for g and makes an appropriate statement about the accuracy of the conclusion.(E) describes an unexpected outcome (e.g. gradient value significantly different from expected value; graph line has an intercept; impossible to draw a graph line that is close to the plotted points) and gives an explanation that is reasonable for why the outcome occurred. (E)