Two pendulums of identical length of 1 m are suspended from the ceiling and begin swinging at the same time. One is at Manila, in the Philippines, where g = 9.784 m/s^2, and the other is at Oslo, Norway, where g = 9.819 m/s^2. After how many oscillations of the Manila pendulum will the two pendulums be in phase again?
The book says it's 561 Oscillations. How do I get that number?
The book says it's 561 Oscillations. How do I get that number?
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First get the period of each.
Tm = 2π√(L/g) = 2.00873 seconds
T9 = 2π√(L/g) = 2.00515
not clear exactly what you mean by "in phase". I interpret it to mean when they both hit the starting point at about the same time.
This may be difficult as we are dealing with irrational numbers.
The difference is 0.00358 sec.
how many cycles does it take for that to equal 2.00873?
2.00873 / 0.00358 = 561.1
checking:
Tm(561) = 1126.898
To(562) = 1126.893 sec
pretty close, but how close does it have to be?
Pendulum period in seconds
T ≈ 2π√(L/g)
L is length of pendulum in meters
g is gravitational acceleration = 9.8 m/s²
Tm = 2π√(L/g) = 2.00873 seconds
T9 = 2π√(L/g) = 2.00515
not clear exactly what you mean by "in phase". I interpret it to mean when they both hit the starting point at about the same time.
This may be difficult as we are dealing with irrational numbers.
The difference is 0.00358 sec.
how many cycles does it take for that to equal 2.00873?
2.00873 / 0.00358 = 561.1
checking:
Tm(561) = 1126.898
To(562) = 1126.893 sec
pretty close, but how close does it have to be?
Pendulum period in seconds
T ≈ 2π√(L/g)
L is length of pendulum in meters
g is gravitational acceleration = 9.8 m/s²