Physics · Oscillations. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.
A body performs simple harmonic motion (SHM) when its acceleration is proportional to its displacement from the mean position and always directed towards that position. The minus sign in a = −ω2x shows this direction.
SHM is linked to circular motion. If a point P moves round a circle at constant angular velocity ω, its projection N on a diameter moves to and fro in SHM. The radius of the circle is the amplitude x0, and the angle ωt that the radius has turned through is the phase, which tells the state of the motion.
At the mean position the speed is greatest and the acceleration is zero. At the extreme positions the speed is zero and the acceleration is greatest.
In a = −16x the number 16 is ω2, not ω. Take the square root first (ω = 4 rad s−1) and then use T = 2π/ω. Also keep the calculator in radians for sin ωt.
Answer: 0.40 m s−1
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