The length of a simple pendulum is 0.75 m and the mass of the particle (the bob)

Question

The length of a simple pendulum is 0.75 m and the mass of the particle (the bob) at the end of the cable is 0.26 kg. The pendulum is pulled away from its equilibrium position by an angle of 8.5° and released from rest. Assume that friction can be neglected and that the resulting oscillatory motion is simple harmonic motion. (a) What
is the angular frequency of the motion? (b) Using the position of the bob at its lowest point as the reference level, determine the total mechanical energy of the pendulum as it swings back and forth. (c) What is the bobs speed as it passes through the lowest point of the swing?

The length of a simple pendulum is 0.75 m and the mass of the particle (the â bobâ ) at the end of the cable is 0.26 kg. The pendulum is pulled away from its equilibrium position by an angle of 8.5Â degree and released from rest. Assume that friction can be neglected and that the resulting oscillatory motion is simple harmonic motion. (a) What is the angular frequency of the motion? (b) Using the position of the bob at its lowest point as the reference level, determine the total mechanical energy of the pendulum as it swings back and forth. (c) What is the bobâ s speed as it passes through the lowest point of the swing?

Explanation / Answer

The mass is irrelevant.
a) 8.5 degrees is just about small enough to use the equation 1/f = T = 2pi x sqr(l/g) [take g=9.8 ms^-2]
b) Total energy = max potential energy = mgh where h = 0.75 - (0.75 x cos(8.5 deg))
c) Total energy = max kinetic energy = 0.5 x m x v^2
and max vel = sqr(answer to b / 0.12)

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