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Unformatted text preview: real world, x A cos(t ) , with A and δ as just determined. Due to our driving having
completely dominated the situation, we have no information left about the initial conditions in this solution.
Intuitively, the amplitude A (as found through its equation) increases with more forcing; that is, F0 is in the
numerator and decreases with more damping (i.e., γ is in the denominator) (12:40). It is often useful to look at
limiting cases, and in this case, very slow motions are instructive. Essentially, in this case the spring will just be
stretched; the inertia of the mass has little effect, so we simply have Hooke’s Law. This corresponds to near-zero
driving frequency. The force just produces extension, and by Hooke’s Law F0=kA (there is no minus sign since we
are dealing with the force on the spring, not its force back as observed in Hooke’s Law in its usual form). So in this
limit, A=F0/k. If we put ω=0 in the A equation, we get A F0...
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