Mechanical Engineering Question:
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How does length and initial angle affect the period in a simple pendulum?
Answer:
The longer the pendulum is the greater the period of each swing. If you increase the length four times, you will double the period.
It is hard to notice, but the period of a pendulum does depend on the angle of oscillation. For small angles, the period is constant and depends only on the length of the pendulum. As the angle of oscillation (amplitude) is increased, additional factors of a Taylor approximation become important. (T=2*pi*sqrt (L/g) [1+theta^2/16+...] and the period increases.
Interestingly, if the pendulum is supported by a very light wire then the mass of the object at the end of the pendulum does not affect the period. Obviously, the greater the mass, the less any air friction, or friction at the pivot will slow the pendulum. Also interestingly, the pendulum period is dependant on the force of gravity on the object (g). One must not assume that g is constant for all places on Earth.
It is hard to notice, but the period of a pendulum does depend on the angle of oscillation. For small angles, the period is constant and depends only on the length of the pendulum. As the angle of oscillation (amplitude) is increased, additional factors of a Taylor approximation become important. (T=2*pi*sqrt (L/g) [1+theta^2/16+...] and the period increases.
Interestingly, if the pendulum is supported by a very light wire then the mass of the object at the end of the pendulum does not affect the period. Obviously, the greater the mass, the less any air friction, or friction at the pivot will slow the pendulum. Also interestingly, the pendulum period is dependant on the force of gravity on the object (g). One must not assume that g is constant for all places on Earth.
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