Chapter 12. Total mechanical energy of a mass oscillating on an ideal spring (12-21)

Question

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{"title":"Total mechanical energy of the oscillating mass–spring system","description":"Correct!","type":"correct","color":"#99CCFF","code":"[{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"1,23,22,48\"}]"} {"title":"Spring constant","description":"Wrong","type":"incorrect","color":"#ffcc00","code":"[{\"shape\":\"rect\",\"coords\":\"118,11,119,13\"},{\"shape\":\"rect\",\"coords\":\"252,21,270,50\"}]"} {"title":"Amplitude of the oscillation","description":"Incorrect","type":"incorrect","color":"#333300","code":"[{\"shape\":\"rect\",\"coords\":\"272,21,292,47\"}]"} {"title":"During the oscillation, the kinetic energy K and spring potential energy U sub spring both change…","description":"Incorrect","type":"incorrect","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"51,18,73,46\"},{\"shape\":\"rect\",\"coords\":\"106,16,131,48\"}]"} {"title":"…but their sum, the total mechanical energy E, always has the same value.","description":"Wrong","type":"incorrect","color":"#333333","code":"[{\"shape\":\"rect\",\"coords\":\"251,20,271,50\"}]"}

Question

8Pcguj2WLnPWW7EWnFYVefMhCJsZI9PHSyvt9iYQrUU=
{"title":"Total mechanical energy of the oscillating mass–spring system","description":"Wrong","type":"incorrect","color":"#99CCFF","code":"[{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"1,23,22,48\"}]"} {"title":"Spring constant","description":"Correct!","type":"correct","color":"#ffcc00","code":"[{\"shape\":\"rect\",\"coords\":\"118,11,119,13\"},{\"shape\":\"rect\",\"coords\":\"252,21,270,50\"}]"} {"title":"Amplitude of the oscillation","description":"Incorrect","type":"incorrect","color":"#333300","code":"[{\"shape\":\"rect\",\"coords\":\"272,21,292,47\"}]"} {"title":"During the oscillation, the kinetic energy K and spring potential energy U sub spring both change…","description":"Incorrect","type":"incorrect","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"51,18,73,46\"},{\"shape\":\"rect\",\"coords\":\"106,16,131,48\"}]"} {"title":"…but their sum, the total mechanical energy E, always has the same value.","description":"Wrong","type":"incorrect","color":"#333333","code":"[{\"shape\":\"rect\",\"coords\":\"251,20,271,50\"}]"}

Question

k+ge5Fuu7eS1VNV2tjIq3jnAU6/KWiNkICa4uewHmf6xzWj2rhL+JCfXB617EtTP
{"title":"Total mechanical energy of the oscillating mass–spring system","description":"Wrong","type":"incorrect","color":"#99CCFF","code":"[{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"1,23,22,48\"}]"} {"title":"Spring constant","description":"Incorrect","type":"incorrect","color":"#ffcc00","code":"[{\"shape\":\"rect\",\"coords\":\"118,11,119,13\"},{\"shape\":\"rect\",\"coords\":\"252,21,270,50\"}]"} {"title":"Amplitude of the oscillation","description":"Correct!","type":"correct","color":"#333300","code":"[{\"shape\":\"rect\",\"coords\":\"272,21,292,47\"}]"} {"title":"During the oscillation, the kinetic energy K and spring potential energy U sub spring both change…","description":"Incorrect","type":"incorrect","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"51,18,73,46\"},{\"shape\":\"rect\",\"coords\":\"106,16,131,48\"}]"} {"title":"…but their sum, the total mechanical energy E, always has the same value.","description":"Wrong","type":"incorrect","color":"#333333","code":"[{\"shape\":\"rect\",\"coords\":\"251,20,271,50\"}]"}

Question

9zmKPcaUwer19sduRqcZBw2XrzZxXde0JE+jpJ6GAW7cip7gHCIC6mT0LPKlVjKHJPEkvwPvWesPNdwnRmGKBb45ZWyw4BVH+diwOZiBp88TEIsnrQSo5oGhwjZGKdQykkPg4ESVvQ9JoPxOIyx+U7Zt9RRTKZqQ
{"title":"Total mechanical energy of the oscillating mass–spring system","description":"Wrong","type":"incorrect","color":"#99CCFF","code":"[{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"1,23,22,48\"}]"} {"title":"Spring constant","description":"Incorrect","type":"incorrect","color":"#ffcc00","code":"[{\"shape\":\"rect\",\"coords\":\"118,11,119,13\"},{\"shape\":\"rect\",\"coords\":\"252,21,270,50\"}]"} {"title":"Amplitude of the oscillation","description":"Wrong","type":"incorrect","color":"#333300","code":"[{\"shape\":\"rect\",\"coords\":\"272,21,292,47\"}]"} {"title":"During the oscillation, the kinetic energy K and spring potential energy U sub spring both change…","description":"Correct!","type":"correct","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"51,18,73,46\"},{\"shape\":\"rect\",\"coords\":\"106,16,131,48\"}]"} {"title":"…but their sum, the total mechanical energy E, always has the same value.","description":"Wrong","type":"incorrect","color":"#333333","code":"[{\"shape\":\"rect\",\"coords\":\"251,20,271,50\"}]"}

Question

694gGdgdSZf1GfbvzcvMzVwi4jmskeOaPAjxHLooLwClVty84NzhcoW9Fpb8G3BkYD3OK6JSBKsEf6UihlO0PTGRB6iqPxC6TOVDsqCZISST9Vv5
{"title":"Total mechanical energy of the oscillating mass–spring system","description":"Wrong","type":"incorrect","color":"#99CCFF","code":"[{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"1,23,22,48\"}]"} {"title":"Spring constant","description":"Incorrect","type":"incorrect","color":"#ffcc00","code":"[{\"shape\":\"rect\",\"coords\":\"118,11,119,13\"},{\"shape\":\"rect\",\"coords\":\"252,21,270,50\"}]"} {"title":"Amplitude of the oscillation","description":"Wrong","type":"incorrect","color":"#333300","code":"[{\"shape\":\"rect\",\"coords\":\"272,21,292,47\"}]"} {"title":"During the oscillation, the kinetic energy K and spring potential energy U sub spring both change…","description":"Wrong","type":"incorrect","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"51,18,73,46\"},{\"shape\":\"rect\",\"coords\":\"106,16,131,48\"}]"} {"title":"…but their sum, the total mechanical energy E, always has the same value.","description":"Correct!","type":"correct","color":"#333333","code":"[{\"shape\":\"rect\",\"coords\":\"251,20,271,50\"}]"}

Review

Equation 12-20 looks like a complicated function of time. But we can simplify it thanks to an important result from trigonometry:

\(sin^2\theta + cos^\theta = 1\) for any value of \(\theta\)