The length of a simple pendulum is 0.74 m and the mass of the particle (the \"bo

Question

The length of a simple pendulum is 0.74 m and the mass of the particle (the "bob") atthe end of the cable is 0.25 kg. Thependulum is pulled away from its equilibrium position by an angleof 9.05° and released from rest.Assume that friction can be neglected and that the resultingoscillatory motion is simple harmonic motion. (a) What is the angular frequency of themotion?
(b) Using the position of the bob at its lowest point as thereference level, determine the total mechanical energy of thependulum as it swings back and forth.
(c) What is the bob's speed as it passes through the lowest pointof the swing? (a) What is the angular frequency of themotion?
(b) Using the position of the bob at its lowest point as thereference level, determine the total mechanical energy of thependulum as it swings back and forth.
(c) What is the bob's speed as it passes through the lowest pointof the swing?

Explanation / Answer

Length L = 0.74 m

Angle = 9.05 degrees

Mass m = 0.25 kg

(a). Angular frequency of the motion w = [ g /L ]

                                                                = 3.639 rad / s

(b). Total mechanical energy E = ( 1/ 2) mw ^ 2 A ^ 2

Where A = amplitude = L sin

               = 0.1163 m

Plug the values we get E = 0.02242 J

(c). Bob’s speed v = Aw

                              = 0.4232 m / s

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