A particle performs motion x = A cosωt. Its instantaneous speed when its position is x is:
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A particle performs motion x = A cosωt. Its instantaneous speed when its position is x is:

G1 Physics · Accepted Answer

For x=Acosωt, v = −Aωsinωt. Using sin²ωt = 1−cos²ωt = 1−x²/A², speed = Aω|sinωt| = ω√(A²−x²).