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Abraham Lincoln University Simple Harmonic Motion Question

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= A cylinder of air has a volume V. = 1.00 L, a pressure Po 1.00 atm, and a temperature of To = 295 K. It is oriented horizontally with ambient atmospheric pressure outside, with an 0.200 kg piston sealing the right side. The piston has face area A = 0.01 m². The piston is displaced 0.1 cm to the right and then released; it begins to oscillate around its original position. Assuming the temperature of the gas is constant, find the angular frequency of oscillation of the piston. Hint: use the Taylor expansion 1 х x+xo хо Gas dxt Activate Windows Go to Settings to activat ++x Thus we have – 2m 2h1 01 = 00 exp (32 1) cos( WT), P(- (25)) Vi = Vho exp (more) 2ho exp 2л cos(2), b 2m b ) w = mw 27 h = ho exp mw a Generally, we see that if a pendulum of mass m and length l is dampened by a force of magnitude bu with an angular frequency w and completes a full oscillation to a height hı, its initial height ho is given by 2b7 ho = h, exp mw We now substitute w = V(wo)2 + (b/2m)2 and wo = g/l to obtain 2b ho = hy exp (m/9/6 +(/2m)
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