a) What is the period of a pendulum oscillating with an amplitude of 5.0 cm? (L=

Question

a) What is the period of a pendulum oscillating with an amplitude of 5.0 cm? (L=1.0 m, m = 0.5 kg)
b) What is the maximum velocity of the bob of the pendulum?
c) What is the energy of the pendulum? Figured out to be 6.1 mJ
d) The pendulum's energy loss (due to damping) is restocked in a clock by allowing a 2.0 kg mass to drop 1.0 m in 1 week. What is the pendulum energy lost during one cycle?
e) Using your answers from (c) and (d) find the percentage of oscillation (pendulum) energy lost in one cycle due to damping.

Explanation / Answer

Given that amplitude A = 5.0 cm Length L =1.0 m , mass m = 0.5 kg a ) Time period of the simple pendulum is T = 2L /g                                                                       = 2 1.0 m / 9.8                                                                        = 2.00s b) maximum velocity of the bob of the pendulum is v = A     angular frequency = 2 / T                                    = 2 / 2.00s                                   = 3.14 rad /s           maximum velocity is v = 5.00*10^-2 m * 3.14 rad /s                                               = 0.517 m/s c ) Energy of the pendulum is E = 1/ 2 k A^2                                                    = 1/2 m ^2 A^2                                                    = 1/2 * 0.5 kg * ( 3.14 )^2 * (5.00*10^-2 )^2                                                    = 6.16*10^-3 J .

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