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

Question 1 of 3

Question

Angular frequency

{"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\"}]"}

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in Section 12-5, $\alpha_z\approx -(g/L)\theta$ (Equation 12-26): The equation is identical except that $g/L$ has been replaced by $mgh/I$ .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 $mgh/I$ :