Title: Advancing Physics AS Teacher Edition
Author: The Institute of Physics
Last saved by: Authorised User
Company: Tasker Milward

Phasors to oscillations
Question 220S: Short Answer |

You will draw out the trace of a sinusoidal oscillation of given frequency and amplitude, starting from a rotating phasor.
How to draw oscillations
You will need a sheet of graph paper, ruler, pair of compasses and protractor. As in the diagram, draw a circle on the left of the paper and graph axes of displacement against time to the right of the circle. Draw the time axis through the centre of the circle.

Divide the circle into twelve 30° sectors, as shown. Divide the time axis of the graph into at least twelve divisions, each representing 0.1 s.

1.	You are going to use a phasor rotating by 30° every 0.1 s. How many degrees does it turn per second? How long will the phasor take to turn through one complete revolution? How many complete revolutions does it make per second?

2.	Choose any marked radius of the circle, and start the phasor off there at time t = 0. Copy across to the graph axes the displacement of the tip of the phasor above the axis, and mark this displacement at t = 0. This step is shown in the diagram. You may start at a different initial angle to that chosen in the diagram.
3.	Go forward in time by 0.1 s. Rotate the phasor anticlockwise (angle to axis increasing) by 30°. Again copy across to the graph axes the new displacement of the tip of the phasor above the axis, and mark this displacement at t = 0.1 s. This step is also shown in the diagram.
4.	Continue to rotate the phasor at 30°. every 0.1 s, and mark the vertical displacement of its tip on the graph, at the appropriate moment in time.
5.	Having completed rotating the phasor through a complete circle, join up the graph points smoothly. What kind of curve have you drawn?

6.	What is the periodic time of the curve you have drawn? What is its frequency?