SHM, unit circle and trig equations

This applet demonstrates SHM motion (mass on an elastic string) as driven by a unit circle. The challenge is to form the equation of motion and solve this to find the first time at which the displacement of the mass is 1m above the x-axis. Notes to teachers: Having allowed students to experiment with the sliders, ask them to give precise verbal descriptions of the observed effects. Students may require some assistance with setting up the equation of motion and perhaps an example together to show the substitution of the displacement with 1 and solving the resulting equation to find t. Check all students are in radian mode on their calculators. Provide other possible configurations of amplitude, phase and ang. velocity and ask students to form and solve trig equations to find t before running the animated model to check. Extension: Ask students to find - the second time the displacement equals 1m - the time between the two occasions at which the displacement equals 1m - the angular velocity at the first and second occasion at which the displacement equals 1m. Can they download and edit the construction to allow negative angular velocities on the slider. What is the effect of this?



Resource Type
amplitude  angular-velocity  circle  equation  phase  trigonometry  unit-circle 
Target Group (Age)
15 – 18
English (United Kingdom)
GeoGebra version
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