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2.5 An undamped oscillator has a natural frequency w, of a rad s-. Various amounts of damping are added to the system to give values of the damping factor y equal to 0.01, 0.30 and 1.0 s-, respectively. (a) For each value of y find the corresponding Q-value and frequency o of the damped oscillations. Comment on the change in w over this range of y. (b) For each of the values of Q. use a spreadsheet program to plot Ao exp(-y1/2) cos cot over the time period t=0 to 10 s, using a value of 10 mm for Ao. (e) Obtain an expression for x for the case of critical danmping with the initial conditions, x 10 mm and dr/dr =0. Plot x over the time period t= 0 to 10 s. %3D %3D

2.5 An undamped oscillator has a natural frequency w, of a rad s-. Various amounts of damping are added to the system to give values of the damping factor y equal to 0.01, 0.30 and 1.0 s-, respectively. (a) For each value of y find the corresponding Q-value and frequency o of the damped oscillations. Comment on the change in w over this range of y. (b) For each of the values of Q. use a spreadsheet program to plot Ao exp(-y1/2) cos cot over the time period t=0 to 10 s, using a value of 10 mm for Ao. (e) Obtain an expression for x for the case of critical danmping with the initial conditions, x 10 mm and dr/dr =0. Plot x over the time period t= 0 to 10 s. %3D %3D

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2.5 An undamped oscillator has a natural frequency w, of n rad s-. Various amounts of damping are added to the system to give values of the damping factor y equal to 0.01, 0.30 and 1.0 s-, respectively. (a) For each value of y find the corresponding Q-value and frequency w of the damped oscillations. Comment on the change in w over this range of y. (b) For each of the values of Q, use a spreadshecet program to plot * = Ao exp(-y1/2) cos ot over the time period1 = 0 to 10 s, using a value of 10 mm for Ao. (c) Obtain an expression for x for the case of critical damping with the initial conditions, x =10 mm and dx/dr = 0. Plot x over the time period i =0 to 10 s. illotion
Transcribed Image Text:2.5 An undamped oscillator has a natural frequency w, of n rad s-. Various amounts of damping are added to the system to give values of the damping factor y equal to 0.01, 0.30 and 1.0 s-, respectively. (a) For each value of y find the corresponding Q-value and frequency w of the damped oscillations. Comment on the change in w over this range of y. (b) For each of the values of Q, use a spreadshecet program to plot * = Ao exp(-y1/2) cos ot over the time period1 = 0 to 10 s, using a value of 10 mm for Ao. (c) Obtain an expression for x for the case of critical damping with the initial conditions, x =10 mm and dx/dr = 0. Plot x over the time period i =0 to 10 s. illotion
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