Chapter 12. Angular frequency of an underdamped oscillation (12-36)

Question

nYGVJ5395/sNTSoZRDHtxXwOG0ailHD0rJ4KXLcGXrK+17jxZ6UVGbe8gn6c12TX1ZOz+6MeMfxRMWQ512zpDQ==

{"title":"Angular frequency of an underdamped mass-spring combination","description":"Correct!","type":"correct","color":"#99CCFF","code":"[{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"3,34,20,56\"}]"} {"title":"Spring constant of the spring","description":"Wrong","type":"incorrect","color":"#ffcc00","code":"[{\"shape\":\"rect\",\"coords\":\"118,11,119,13\"},{\"shape\":\"rect\",\"coords\":\"141,11,159,41\"}]"} {"title":"Damping coefficient","description":"Incorrect","type":"incorrect","color":"#333300","code":"[{\"shape\":\"rect\",\"coords\":\"214,12,231,35\"}]"} {"title":"Mass of the oscillating object","description":"Incorrect","type":"incorrect","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"220,49,245,67\"},{\"shape\":\"rect\",\"coords\":\"137,52,162,69\"}]"}

Question

J3lmwXb0Ma5D/sx/8TjIAJyvpe1+ZRQqXkZEHcd9y1i454+Y

{"title":"Angular frequency of an underdamped mass-spring combination","description":"Incorrect","type":"incorrect","color":"#99CCFF","code":"[{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"3,34,20,56\"}]"} {"title":"Spring constant of the spring","description":"Correct!","type":"correct","color":"#ffcc00","code":"[{\"shape\":\"rect\",\"coords\":\"118,11,119,13\"},{\"shape\":\"rect\",\"coords\":\"141,11,159,41\"}]"} {"title":"Damping coefficient","description":"Incorrect","type":"incorrect","color":"#333300","code":"[{\"shape\":\"rect\",\"coords\":\"214,12,231,35\"}]"} {"title":"Mass of the oscillating object","description":"Incorrect","type":"incorrect","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"220,49,245,67\"},{\"shape\":\"rect\",\"coords\":\"137,52,162,69\"}]"}

Question

eJcxDKY/CmDNc5tguAMWun+uSApY6Zot

{"title":"Angular frequency of an underdamped mass-spring combination","description":"Incorrect","type":"incorrect","color":"#99CCFF","code":"[{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"3,34,20,56\"}]"} {"title":"Spring constant of the spring","description":"Wrong","type":"incorrect","color":"#ffcc00","code":"[{\"shape\":\"rect\",\"coords\":\"118,11,119,13\"},{\"shape\":\"rect\",\"coords\":\"141,11,159,41\"}]"} {"title":"Damping coefficient","description":"Correct!","type":"correct","color":"#333300","code":"[{\"shape\":\"rect\",\"coords\":\"214,12,231,35\"}]"} {"title":"Mass of the oscillating object","description":"Incorrect","type":"incorrect","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"220,49,245,67\"},{\"shape\":\"rect\",\"coords\":\"137,52,162,69\"}]"}

Question

lGd1Kr/5BXRG2EgSytp0DJEn4SJRg8ge2JQP7DmZGSfu/RpG

{"title":"Angular frequency of an underdamped mass-spring combination","description":"Incorrect","type":"incorrect","color":"#99CCFF","code":"[{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"3,34,20,56\"}]"} {"title":"Spring constant of the spring","description":"Wrong","type":"incorrect","color":"#ffcc00","code":"[{\"shape\":\"rect\",\"coords\":\"118,11,119,13\"},{\"shape\":\"rect\",\"coords\":\"141,11,159,41\"}]"} {"title":"Damping coefficient","description":"Wrong","type":"incorrect","color":"#333300","code":"[{\"shape\":\"rect\",\"coords\":\"214,12,231,35\"}]"} {"title":"Mass of the oscillating object","description":"Correct!","type":"correct","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"220,49,245,67\"},{\"shape\":\"rect\",\"coords\":\"137,52,162,69\"}]"}

Review

Figure 12-16 is a graph of this function. The decreasing amplitude means that the oscillating object makes smaller and smaller excursions around the equilibrium position as time goes by.

The presence of the damping force also changes the oscillation angular frequency from the value \(\omega = \sqrt{k/m}\) without damping. With damping present, the angular frequency is