Chapter 12. Angular frequency, period, and frequency for a physical pendulum (small amplitude) (12-31)

Question

74ZQsRWNs5eaxFMtu1ST1zsHSXQD2A/8
{"title":"Angular frequency","description":"Correct!","type":"correct","color":"#99CCFF","code":"[{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"2,29,23,50\"}]"} {"title":"Period","description":"Wrong","type":"incorrect","color":"#ffcc00","code":"[{\"shape\":\"rect\",\"coords\":\"118,11,119,13\"},{\"shape\":\"rect\",\"coords\":\"1,124,19,148\"}]"} {"title":"Frequency","description":"Incorrect","type":"incorrect","color":"#333300","code":"[{\"shape\":\"rect\",\"coords\":\"1,221,16,257\"}]"}

Question

i3GYZUGh83sgFQrZ
{"title":"Angular frequency","description":"Wrong","type":"incorrect","color":"#99CCFF","code":"[{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"2,29,23,50\"}]"} {"title":"Period","description":"Correct!","type":"correct","color":"#ffcc00","code":"[{\"shape\":\"rect\",\"coords\":\"118,11,119,13\"},{\"shape\":\"rect\",\"coords\":\"1,124,19,148\"}]"} {"title":"Frequency","description":"Incorrect","type":"incorrect","color":"#333300","code":"[{\"shape\":\"rect\",\"coords\":\"1,221,16,257\"}]"}

Question

6AjRK1rC+/08Tcq8CY6Akw==
{"title":"Angular frequency","description":"Wrong","type":"incorrect","color":"#99CCFF","code":"[{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"2,29,23,50\"}]"} {"title":"Period","description":"Incorrect","type":"incorrect","color":"#ffcc00","code":"[{\"shape\":\"rect\",\"coords\":\"118,11,119,13\"},{\"shape\":\"rect\",\"coords\":\"1,124,19,148\"}]"} {"title":"Frequency","description":"Correct!","type":"correct","color":"#333300","code":"[{\"shape\":\"rect\",\"coords\":\"1,221,16,257\"}]"}

Review

Compare Equation 12-30 to the corresponding equation for the simple pendulum that we derived in Section 12-5, \(\alpha_z\approx -(g/L)\theta\) (Equation 12-26): The equation is identical except that \(g/L\) has been replaced by \(mgh/I\). So we conclude that just as for the simple pendulum, the oscillations of a physical pendulum are simple harmonic motion provided that the amplitude is relatively small. To find the angular frequency, period, and frequency of a physical pendulum, we simply take Equations 12-27 for a simple pendulum and replace \(g/L\) with \(mgh/I\):