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Homework Statement
Two identical simple pendulums, of length 0.25 m and period T, are mounted side-by-side. One is released from rest with an initial angular displacement of π/9 rad, and the other is started with an initial angular velocity of 0.1 rad/s at θ = 0. They are both started in motion simultaneously. Which of the following statements are true?
A: The equation of motion for both oscillators reads: x = Acos(ωt+δ)
B: After 0.6 seconds they differ in phase by π.
C: After a time of T, they both return to their initial displacement.
D: They both have the same amplitude.
Homework Equations
x(t)=Acos(ωt+δ)
The Attempt at a Solution
What I'm really confused about is the initial angular velocity for the second pendulum. How does this work exactly? Like how do I incorporate it into my equations? The "natural" ω would be √(g/L)≈6.3rad/s. So is the second one driven?
Anyways
A: True this is the equation of motion for all pendulums, right? Or is it False because for the second one, it's "pushed" at first?
B: True. δ=0 for the first one since its initial position is it's amplitude (at t=0) and δ=pi for the second one since sinpi=0, so they always differ in phase by pi (unless that initial angular speed messes that up)
C:True? since this is the definition of a period. Or is it false, again because of the initial angular speed.
D: I don't know how to figure this out, except that the first has one of pi/9rad
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