A simple pendulum of length 1.85m and mass 1.51 kg is set into motion oscillatin

Question

A simple pendulum of length 1.85m and mass 1.51 kg is set into motion oscillating back and forth. The maximum velocity achieved by the pendulum is 0.736 m/s. part A From what initial height was the pendulum released? This height is the height above the lowest point in the pendulum swing. h = Part B What initial arclength was the pendulum pulled from equilibrium? s = Answer Requested Part C How many oscillations has the pendulum swung through during the first 15 seconds? Express your answer for the number of oscillations to 3 significant figures. N = Part D Assuming that the pendulum was pulled to the right and then released, what velocity would the pendulum bob have 21.2 seconds after release? You may assume that air resistance has a negligible effect on the pendulum. v =

Explanation / Answer

from conservation of energy, we know KE= PE
1/2mv2 = mgh

h=v2/2g = 0.7362 /2*9.8=0.027m

Angle subtended at hinge : L(1-cos())=h

=9.8 degree =0.171 radians

Arc length = Lrad = 1.85*0.171= 0.316 m

Time period = 2root(L/g) = 2.73 sec

in 15 sec , pendulum will have completed 5 complete oscillations. exactly = 5.49 oscillations

21.2 sec = 7.76 time periods

Same as velocity at 2 ( 21.2 mod 2.73) secs after release.

Write the speed as V=0.736sin(t). at t=2 , =2/T => v= 0.736 sin(263.73 deg)= - 0.731 m/s ,i.e, in opposite direction

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