SHM, unit circle and trig equations
Run the animation below (click the play arrow at the bottom left of the graphics view) to see how the amplitude, phase and angular velocity controls the vertical displacement of the mass on an elastic string at a given time (and how this equation of motion is driven by the unit circle).
Now try to write down the equation of motion for the displacement of the (centre of the) mass above the x-axis at time t seconds. This motion is called Simple Harmonic Motion (SHM). Can you use your equation to find the first time that this displacement = 1 metre (the horizontal dotted line) a) for the initial configuration [amplitude = 1m, phase = 0 rad, angular velocity = 1 rad/s] b) for other configurations that your teacher will tell you. Test these predictions by running the animated model. Finally, differentiate your equation of motion twice to find an expression for the acceleration of the mass at time t and hence show that the acceleration is proportional to the displacement. Which was is the acceleration directed?