a simple pendulum with a length of 1.73 m and a mass of 6.69kg is given an initi

Question

a simple pendulum with a length of 1.73 m and a mass of 6.69kg is given an initial speed of 1.16 m/s at its equilibriumposition. a)assuming it undergoes simple harmonic motion, determine itsperiod.   (s) b)determine its total energy. (J) c) determine its maximum angular displacement. (For large vand/or small I the small angle approximation may not be good enoughhere.) please explain how you got your answers. thanks! a simple pendulum with a length of 1.73 m and a mass of 6.69kg is given an initial speed of 1.16 m/s at its equilibriumposition. a)assuming it undergoes simple harmonic motion, determine itsperiod.   (s) b)determine its total energy. (J) c) determine its maximum angular displacement. (For large vand/or small I the small angle approximation may not be good enoughhere.) please explain how you got your answers. thanks!

Explanation / Answer

Length L = 1.73 m mass m = 6.69 kg Initial speed V = 1.16 m / s (a). period T = 2 [ L / g ]                     = 2.6399 s (b). Total energy E = ( 1/ 2) m w ^ 2 A ^ 2                               = ( 1/ 2) m V ^2          Since V = Aw                               =4.5 J (c).we know amplitude A = V / w                                          = V / ( 2 /T )                                          = VT / 2                                          = 0.4873 m Maximum angular displacement = A/L                                                    = 0.2817 rad

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