1. a) If the amplitude is large, will the resultant period be greater than, less

Question

1. a) If the amplitude is large, will the resultant period be greater than, less than, or equal to the period for small amplitudes? Explain.
b) In general, if the entire mass of a physical pendulum is imagined to be moved to the center of mass, will the period of this simple pendulum be greater than, less than, or equal to the original period? Explain.
c) In general, if the entire mass of a physical pendulum is imagined to be moved to a position equal to the radius of gyration away from the axis of rotation, will the period of this simple pendulum be greater than, less than, or equal to the original period? Explain.
1. a) If the amplitude is large, will the resultant period be greater than, less than, or equal to the period for small amplitudes? Explain.
b) In general, if the entire mass of a physical pendulum is imagined to be moved to the center of mass, will the period of this simple pendulum be greater than, less than, or equal to the original period? Explain.
c) In general, if the entire mass of a physical pendulum is imagined to be moved to a position equal to the radius of gyration away from the axis of rotation, will the period of this simple pendulum be greater than, less than, or equal to the original period? Explain.
1. a) If the amplitude is large, will the resultant period be greater than, less than, or equal to the period for small amplitudes? Explain.
b) In general, if the entire mass of a physical pendulum is imagined to be moved to the center of mass, will the period of this simple pendulum be greater than, less than, or equal to the original period? Explain.
c) In general, if the entire mass of a physical pendulum is imagined to be moved to a position equal to the radius of gyration away from the axis of rotation, will the period of this simple pendulum be greater than, less than, or equal to the original period? Explain.

Explanation / Answer

1. a. for large amplitudes
the acceleration due to gravity is not the same for the igher points, and hence the acceleration is slower
hence, the time period is larger for large amplitudes than the time period determined theoertically using small amplitude approximation

b. in general if mass of the entire pendulum is moved to the center of mass, the time period of the pendulum will be the same, as we take the mass, and the distance of the center of the mass fomr the pivot point

c. if the entire mass is moved to the radius of gyration
  then
  radius of gyration k < length of pendulum
  hence
  time period of the p[endulum decreases form the formula T = 2*pisqrt()

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