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I know that there are many ways to derive the equations for SHM. I'm clear on how the negative signs come out when we use derivatives; but I've a problem understanding how the negative signs come into play using the reference circle.

1. If the centripetal acceleration is a = rω^{2}, why is it that the SHM acceleration or the x component of centripetal accleration becomes -rω^{2}cosθ and not rω^{2}cosθ? The direction of the x component of the centripetal acceleration is correct, why do we need to include the negative sign?

2. Similarly, when considering the tangential velocity of a particle undergoing uniform circular motion, why is the SHM velocity -rωsinθ and not rωsinθ?

Thanks in advance!

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# SHM derivation

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