k time A one squared. In the second case after over there is some dampening after ~ one oscillation, it'll it is in one fifty percent times k times the brand-new amplitude A 2 squared. We're told that A two is going to be three percent less than A one. For this reason amplitude 2 is A one minus 0.03 times A one which is 0.97 A one. We can substitute 0.97 A one, for this reason amplitude 2 is walking to it is in 97 percent the what amplitude one was. We'll substitute the in for A two here. This functions out to 0.9409 i beg your pardon is what 0.97 squared is, multiply by one half k A one. One fifty percent k A one squared is potential energy one. So i substitute that here. Potential power two is 0.9409 time potential power one. The percent readjust is going to it is in potential power two minus potential energy one, separated by ns E one times 100 percent. That's 0.9409 ns E one the we figured out just now for p E two, minus ns E one over ns E one. The p E one's cancel and also this turns into a number one and so 0.9409 minus one time 100 percent is negative 5.91 percent. For this reason 5.91 percent the potential energy is lost throughout each oscillation.">


You are watching: The amplitude of a lightly damped harmonic oscillator decreases by 3.0% during each cycle.

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This is college Physics Answers with Shaun Dychko. The preferably potential energy of a an easy harmonic oscillator is one half times the feather constant, time the amplitude squared. So in the very first case we have actually one fifty percent k time A one squared. In the 2nd case after there is part dampening after one oscillation, it"ll it is in one half times k times the brand-new amplitude A 2 squared. We"re told that A two is going to be three percent much less than A one. For this reason amplitude 2 is A one minus 0.03 time A one i m sorry is 0.97 A one. We deserve to substitute 0.97 A one, so amplitude 2 is going to be 97 percent the what amplitude one was. We"ll substitute the in because that A two here. This works out to 0.9409 i beg your pardon is what 0.97 squared is, multiply by one half k A one. One fifty percent k A one squared is potential energy one. So ns substitute the here. Potential power two is 0.9409 time potential power one. The percent readjust is walk to be potential power two minus potential power one, split by p E one times 100 percent. That"s 0.9409 p E one that we established just currently for p E two, minus ns E one over ns E one. The p E one"s cancel and this turns into a number one and also so 0.9409 minus one time 100 percent is an unfavorable 5.91 percent. For this reason 5.91 percent the potential energy is lost throughout each oscillation.
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