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(II) For a forced oscillation at resonance $\left(\omega=\omega_{0}\right),$ what is the value of the phase angle $\phi_{0}$ in Eq. 22$?$ (b) What, then, is the displacement at a time when the driving force $F_{\text { ext }}$ is a maximum, and at a time when $F_{\text { ext }}=0 ?$ (c) What is the phase difference (in degrees) between the driving force and the displacement in this case?$x=A_{0} \sin \left(\omega t+\phi_{0}\right)$

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a. 0b. $$\pm A_{0}$$c. The phase difference between the driving force and the displacement in this case is $90^{\circ}$

04:31

Shital Rijal

Physics 101 Mechanics

Chapter 14

Oscillators

Motion Along a Straight Line

Motion in 2d or 3d

Periodic Motion

Cornell University

Simon Fraser University

University of Winnipeg

Lectures

04:01

2D kinematics is the study of the movement of an object in two dimensions, usually in a Cartesian coordinate system. The study of the movement of an object in only one dimension is called 1D kinematics. The study of the movement of an object in three dimensions is called 3D kinematics.

02:18

In physics, an oscillation is the repetitive variation, typically in time, of some measure about a central value or between two or more different states. The oscillation may be periodic or aperiodic.

01:52

A damped harmonic oscillat…

03:31

The graph shows the power …

04:12

(II) Determine the phase c…

01:06

In forced oscillation of a…

03:35

A $5.0-\mathrm{kg}$ object…

in this problem on the topic of oscillators, we want to calculate the phase angle phi not for a forced oscillation at resonance. That is when omega is equal to omega not. We then want to know the displacement at a time when the driving force is a maximum and every time when the driving force is equal to zero. Lastly, we want to know the phase difference between the driving force and the displacement in this case. Now we can calculate the phase angle phi not using the equation that we've learned and this is the oct 10 of omega. North squared minus omega squared divided by omega and to be over them. But remember at resonance we have omega to be omega, not terrorism and angular frequency. This means that the fire angle but the phase angle rather fine not is equal to the oct 10 of omega. North squared minus omega. North squared divided by omega to be over. Em we can see that this is simply equal to zero and so they phase difference zero next for part B. You want to know the displacement when the driving forces a maximum and the displacement when the driving force is equal to zero. If we have omega equal to omega, not at the resonant frequency, we had this driving force if E X. T. To be if not call sign, Oh, Megan at times T. And the displacement X is equal to may not same omega note times T. Now the displacement and the driving force a quarter cycle or 90 degrees out of phase with each other. So this means that the displacement X is equal to zero when the driving force is a maximum and the displacement is a maximum when the driving force zero. Lastly in part C. This problem, you want to know the phase difference between the driving force and the displacement and as mentioned above. The phase difference Bye is equal to 90 degrees

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