Arrey, the a = -ω²x test is straightforward: if your acceleration equation can be forced into that exact form, with ω as a positive constant, it's SHM. But yaar, don't just memorize the test — feel the rhythm! Teaching kids the harmonium showed me that the restoring force, like a perfect chord, must be precisely proportional and pulling back to that one fixed point. My old, glitching microphone taught me the hard way: if the equation has extra terms or the constant isn't square, the motion won't be that pure, simple oscillation.
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