Physics A2 · Oscillations. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.
An oscillation is a repeated to-and-fro motion about an equilibrium position. Simple harmonic motion (s.h.m.) is the special case in which the acceleration is proportional to the displacement from a fixed point and is always directed towards that point: a = −ω2x.
The minus sign means the acceleration is opposite to the displacement. At the equilibrium position the displacement and acceleration are zero and the speed is greatest. At maximum displacement (the amplitude, x0) the speed is zero and the acceleration is greatest.
On graphs against time, velocity is the gradient of the displacement graph and leads displacement by a quarter of a cycle. Acceleration is the displacement graph turned upside down.
Students leave the calculator in degrees when using x = x0 sin ωt. Here ωt is in radians, so switch the calculator to radian mode first.
Answer: Maximum speed 0.79 m s−1; speed at 0.030 m is 0.63 m s−1.
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