Physics · Mathematical methods and mechanics. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.
In simple harmonic motion the acceleration is proportional to the displacement and directed towards equilibrium: a = −ω2x. Energy passes between kinetic and potential forms while the total stays constant. Damping removes energy, so the amplitude dies away; critical damping brings the system back to rest in the shortest time without oscillating. Resonance is the large amplitude that appears when the driving frequency matches the natural frequency. Less damping gives a taller, sharper peak.
A wave carries energy without carrying matter. When waves meet, their displacements add. A path difference of nλ gives a maximum and (n + ½)λ gives a minimum. Two equal waves travelling in opposite directions form a standing wave with fixed nodes and antinodes. Only transverse waves can be polarised, so sound cannot.
Giving a closed pipe all the harmonics. A pipe closed at one end has L = λ/4 for its fundamental and sounds only the odd multiples (f, 3f, 5f).
Answer: T = 0.31 s, maximum speed 2 m s−1, energy 1 J.
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