![]() It has a function x(t), and it's second derivative d 2x dt 2 The spring pulls it back up based on how stretched it is ( k is the spring's stiffness, and x is how stretched it is): F = -kx The weight is pulled down by gravity, and we know from Newton's Second Law that force equals mass times acceleration:Īnd acceleration is the second derivative of position with respect to time, so:
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