Chapter 12. Amplitude of a damped, driven oscillation (12-42)

Question

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Question

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{"title":"Amplitude of a mass-spring system driven by a force F(t) = F sub 0 cos omega t","description":"Wrong","type":"incorrect","color":"#99CCFF","code":"[{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"1,19,18,43\"}]"} {"title":"Maximum magnitude of the driving force","description":"Correct!","type":"correct","color":"#ffcc00","code":"[{\"shape\":\"rect\",\"coords\":\"118,11,119,13\"},{\"shape\":\"rect\",\"coords\":\"162,1,180,25\"}]"} {"title":"Damping coefficient","description":"Incorrect","type":"incorrect","color":"#333300","code":"[{\"shape\":\"rect\",\"coords\":\"240,45,257,68\"}]"} {"title":"Driving angular frequency","description":"Incorrect","type":"incorrect","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"268,52,286,70\"},{\"shape\":\"rect\",\"coords\":\"163,49,187,71\"}]"} {"title":"Natural angular frequency","description":"Incorrect","type":"incorrect","color":"#333333","code":"[{\"shape\":\"rect\",\"coords\":\"103,52,128,69\"}]"} {"title":"Mass of the oscillating object","description":"Wrong","type":"incorrect","color":"#800000","code":"[{\"shape\":\"rect\",\"coords\":\"64,53,90,68\"}]"}

Question

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{"title":"Amplitude of a mass-spring system driven by a force F(t) = F sub 0 cos omega t","description":"Wrong","type":"incorrect","color":"#99CCFF","code":"[{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"1,19,18,43\"}]"} {"title":"Maximum magnitude of the driving force","description":"Incorrect","type":"incorrect","color":"#ffcc00","code":"[{\"shape\":\"rect\",\"coords\":\"118,11,119,13\"},{\"shape\":\"rect\",\"coords\":\"162,1,180,25\"}]"} {"title":"Damping coefficient","description":"Correct!","type":"correct","color":"#333300","code":"[{\"shape\":\"rect\",\"coords\":\"240,45,257,68\"}]"} {"title":"Driving angular frequency","description":"Incorrect","type":"incorrect","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"268,52,286,70\"},{\"shape\":\"rect\",\"coords\":\"163,49,187,71\"}]"} {"title":"Natural angular frequency","description":"Incorrect","type":"incorrect","color":"#333333","code":"[{\"shape\":\"rect\",\"coords\":\"103,52,128,69\"}]"} {"title":"Mass of the oscillating object","description":"Wrong","type":"incorrect","color":"#800000","code":"[{\"shape\":\"rect\",\"coords\":\"64,53,90,68\"}]"}

Question

/A2G175fvgJBuTLKtEM/lJHLFY04eVUq/VGb8nuxULI=
{"title":"Amplitude of a mass-spring system driven by a force F(t) = F sub 0 cos omega t","description":"Wrong","type":"incorrect","color":"#99CCFF","code":"[{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"1,19,18,43\"}]"} {"title":"Maximum magnitude of the driving force","description":"Incorrect","type":"incorrect","color":"#ffcc00","code":"[{\"shape\":\"rect\",\"coords\":\"118,11,119,13\"},{\"shape\":\"rect\",\"coords\":\"162,1,180,25\"}]"} {"title":"Damping coefficient","description":"Incorrect","type":"incorrect","color":"#333300","code":"[{\"shape\":\"rect\",\"coords\":\"240,45,257,68\"}]"} {"title":"Driving angular frequency","description":"Correct!","type":"correct","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"268,52,286,70\"},{\"shape\":\"rect\",\"coords\":\"163,49,187,71\"}]"} {"title":"Natural angular frequency","description":"Incorrect","type":"incorrect","color":"#333333","code":"[{\"shape\":\"rect\",\"coords\":\"103,52,128,69\"}]"} {"title":"Mass of the oscillating object","description":"Wrong","type":"incorrect","color":"#800000","code":"[{\"shape\":\"rect\",\"coords\":\"64,53,90,68\"}]"}

Question

0hrLlnzMvMgmRzCc7QyzKyKtqXH3Qdq0a2FHSRpKs8E=
{"title":"Amplitude of a mass-spring system driven by a force F(t) = F sub 0 cos omega t","description":"Wrong","type":"incorrect","color":"#99CCFF","code":"[{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"1,19,18,43\"}]"} {"title":"Maximum magnitude of the driving force","description":"Incorrect","type":"incorrect","color":"#ffcc00","code":"[{\"shape\":\"rect\",\"coords\":\"118,11,119,13\"},{\"shape\":\"rect\",\"coords\":\"162,1,180,25\"}]"} {"title":"Damping coefficient","description":"Incorrect","type":"incorrect","color":"#333300","code":"[{\"shape\":\"rect\",\"coords\":\"240,45,257,68\"}]"} {"title":"Driving angular frequency","description":"Wrong","type":"incorrect","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"268,52,286,70\"},{\"shape\":\"rect\",\"coords\":\"163,49,187,71\"}]"} {"title":"Natural angular frequency","description":"Correct!","type":"correct","color":"#333333","code":"[{\"shape\":\"rect\",\"coords\":\"103,52,128,69\"}]"} {"title":"Mass of the oscillating object","description":"Wrong","type":"incorrect","color":"#800000","code":"[{\"shape\":\"rect\",\"coords\":\"64,53,90,68\"}]"}

Question

lGd1Kr/5BXRG2EgSytp0DJEn4SJRg8ge2JQP7DmZGSfu/RpG
{"title":"Amplitude of a mass-spring system driven by a force F(t) = F sub 0 cos omega t","description":"Wrong","type":"incorrect","color":"#99CCFF","code":"[{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"1,19,18,43\"}]"} {"title":"Maximum magnitude of the driving force","description":"Incorrect","type":"incorrect","color":"#ffcc00","code":"[{\"shape\":\"rect\",\"coords\":\"118,11,119,13\"},{\"shape\":\"rect\",\"coords\":\"162,1,180,25\"}]"} {"title":"Damping coefficient","description":"Incorrect","type":"incorrect","color":"#333300","code":"[{\"shape\":\"rect\",\"coords\":\"240,45,257,68\"}]"} {"title":"Driving angular frequency","description":"Wrong","type":"incorrect","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"268,52,286,70\"},{\"shape\":\"rect\",\"coords\":\"163,49,187,71\"}]"} {"title":"Natural angular frequency","description":"Incorrect","type":"incorrect","color":"#333333","code":"[{\"shape\":\"rect\",\"coords\":\"103,52,128,69\"}]"} {"title":"Mass of the oscillating object","description":"Correct!","type":"correct","color":"#800000","code":"[{\"shape\":\"rect\",\"coords\":\"64,53,90,68\"}]"}

Review

As was the case for Equation 12-34, the equation for damped oscillations without a driving force that we presented in Section 12-7, solving Equation 12-41 is beyond our scope. But here’s what the solutions are like: When the driving force is first applied, the motion is a complicated combination of an oscillation at the angular frequency \(\omega_{\mathrm{damped}}\) given by Equation 12-39 and an oscillation at the driving angular frequency \(\omega\). The oscillation at \(\omega_{\mathrm{damped}}\) quickly dies away (it’s a damped oscillation), and the system is left oscillating at the driving angular frequency \(\omega\) The amplitude of these oscillations is