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Damped Oscillator Consider a 5. weakly damped oscillator with B < wo. There is a little difficulty defining the "period" Ti since the motion is not periodic However, a definition that makes sense is that T1 is the time between successive maxima of r(t) (a) Make a sketch of x(t) against t and indicate this definition of T1 on your graph. Show that T1 27T/w1 (b) Show that an zeros of xt). Show this one on your sketch. (c) If B = wo/2, by what factor does the amplitude shrink in one period? equivalent definition is that Ti is twice the time between successive 11

Damped Oscillator Consider a 5. weakly damped oscillator with B < wo. There is a little difficulty defining the "period" Ti since the motion is not periodic However, a definition that makes sense is that T1 is the time between successive maxima of r(t) (a) Make a sketch of x(t) against t and indicate this definition of T1 on your graph. Show that T1 27T/w1 (b) Show that an zeros of xt). Show this one on your sketch. (c) If B = wo/2, by what factor does the amplitude shrink in one period? equivalent definition is that Ti is twice the time between successive 11

Classical Dynamics of Particles and Systems
Classical Dynamics of Particles and Systems
5th Edition
ISBN:9780534408961
Author:Stephen T. Thornton, Jerry B. Marion
Publisher:Stephen T. Thornton, Jerry B. Marion
Chapter3: Oscillations
Section: Chapter Questions
Problem 3.31P
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Damped Oscillator Consider a 5. weakly damped oscillator with B < wo. There is a little difficulty defining the "period" Ti since the motion is not periodic However, a definition that makes sense is that T1 is the time between successive maxima of r(t) (a) Make a sketch of x(t) against t and indicate this definition of T1 on your graph. Show that T1 27T/w1 (b) Show that an zeros of xt). Show this one on your sketch. (c) If B = wo/2, by what factor does the amplitude shrink in one period? equivalent definition is that Ti is twice the time between successive 11
Transcribed Image Text:Damped Oscillator Consider a 5. weakly damped oscillator with B < wo. There is a little difficulty defining the "period" Ti since the motion is not periodic However, a definition that makes sense is that T1 is the time between successive maxima of r(t) (a) Make a sketch of x(t) against t and indicate this definition of T1 on your graph. Show that T1 27T/w1 (b) Show that an zeros of xt). Show this one on your sketch. (c) If B = wo/2, by what factor does the amplitude shrink in one period? equivalent definition is that Ti is twice the time between successive 11
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