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$\bullet$ $\bullet$ (a) If a vibrating system has total energy $E_{0},$ what will its total \right. energy be (in terms of $E_{0} )$ if you double the amplitude of vibration? (b) If you want to triple the total energy of a vibrating system with amplitude $A_{0},$ what should its new amplitude be (in terms of $A_{0} ) ?$

a) 4$E_{0_{1}}$b) $\sqrt{3} A_{0_{1}}$

Physics 101 Mechanics

Chapter 11

Elasticity and Periodic Motion

Equilibrium and Elasticity

Periodic Motion

University of Washington

University of Winnipeg

McMaster University

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in this problem, we're going to use the relationship between the total energy and the amplitude. And so if we set up two systems like this, easy go 1/2 case where any non is equal to 1/2 k not square. And I let a go to twice the amplitude of a Not Then we want to figure out what is in terms of, you know, and the way we figure this out, it wasn't We just plug in this into this, so it is equal to 1/2 okay, a squared. And so today I'm gonna plug into a knot square. This suffice to 1/2 k times for a not squared. And then I'm just gonna pull this for out front to get four times 1/2 que es not squared. But 1/2 que es, not squared is seen on. So this is equal to 40 knot. So we see whenever is to a not that easy go through four times, you know, so doubling the amplitude pleasurable. Seeing she involved for part B, we have that he is equal to three e non and we want to figure out the relationship between the amplitude is playing in the forms of the energy. Here we get that 1/2 K a square is equal to three times 1/2 k. Hey, not squared and say not there. So you canceled occasion when you cancel that one house immediately and we get a squared is equal to three a non squared or a physical today, not times 33 and that's answer.

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