T = 2pi*SQRT(L/g). or. T = 2π√(L/g). where. 1 T is the period in seconds (s). 2 pi = 3.14 (it is also written as the Greek letter π).
The time for one complete cycle, a left swing and a right swing, is called the period. The period depends on the length of the pendulum, and also to a slight degree on the amplitude, the width of the pendulum's swing. The simple gravity pendulum is an idealized mathematical model of a pendulum. This is a weight (or bob) on the end of a massless cord suspended from a pivot, without friction. When given an initial push, it will swing back and forth at a constant amplitude. Or more concisely by the substitution expressing in terms of, (). where is the complete elliptic integral of the first kind defined by. For comparison of the approximation to the full solution, consider the period of a pendulum of length 1 m on Earth (g = 9.80665 m/s 2) at initial angle 10 degrees is. The linear approximation gives. The motion is simple harmonic motion where θ 0 is the semi-amplitude of the oscillation (that is, the maximum angle between the rod of the pendulum and the vertical). The period of the motion, the time for a complete oscillation (outward and return) is. which is known as Christiaan Huygens 's law for the period. (). where is the complete elliptic integral of the first kind defined by. For comparison of the approximation to the full solution, consider the period of a pendulum of length 1 m on Earth (g = 9.80665 m/s 2) at initial angle 10 degrees is. 6. Use Figure 1 to estimate the period of a pendulum with a length of 90 cm and a mass of 200.0 grams that is released from an angle of 30°. a. 1.88 seconds b. 2.00 seconds c. 2.14 seconds d. 2.90 seconds 7. A 130-cm length pendulum consisting of a 200.0-gram mass is released from an angle of 30°. Use Figure 2 to estimate the period of a pendulum with a length of 65 cm and a mass of 400.0 grams that is released from an angle of 30°. a. 0.81 seconds b. 1.30 seconds c. 1.63 seconds d. Nonsense! It is impossible to make such an estimate since no pattern exists. 11. T = s. Note that the angular amplitude does not appear in the expression for the period. This expression for period is reasonably accurate for angles of a few degrees, but the treatment of the large amplitude pendulum is much more complex. For the physical pendulum with distributed mass, the distance from the point of support to the center of mass is the determining length and the period is affected by the distribution of mass as expressed in the moment of inertia I. The equation for the period of a simple pendulum starting at a small angle (a) is: T = 2pi*SQRT(L/g). or. T = 2π√(L/g). where. 1  T is the period in seconds (s). 2  pi = 3.14 (it is also written as the Greek letter π). Equations for period and frequency. The period of the motion for a pendulum is how long it takes to swing back-and-forth, measured in seconds. Period is designated as T. The frequency of a pendulum is how many back-and-forth swings there are in a second, measured in hertz. Frequency is usually designated as f. A simple pendulum is one which can be considered to be a point mass suspended from a string or rod of negligible mass. It is a resonant system with a single resonant frequency. For small amplitudes, the period of such a pendulum can be approximated by: For the physical pendulum with distributed mass, the distance from the point of support to the center of mass is the determining length and the period is affected by the distribution of mass as expressed in the moment of inertia I. The period for a simple pendulum does not depend on the mass or the initial anglular displacement, but depends only on the length L of the string and the value of the gravitational field strength g, according to The mpeg movie at left (39.5 kB) shows two pendula, with different lengths. With the assumption of small angles, the frequency and period of the pendulum are independent of the initial angular displacement amplitude. All simple pendulums should have the same period regardless of their initial angle (and regardless of their masses).
https://en.wikipedia.org/wiki/Pendulum https://en.wikipedia.org/wiki/Pendulum_(mathematics) https://en.wikipedia.org/wiki/Pendulum_(mathematics) http://www.physicsclassroom.com/getattachment/reasoning/waves/src28.pdf http://hyperphysics.phy-astr.gsu.edu/hbase/pend.html http://www.school-for-champions.com/science/pendulum_equations.htm http://hyperphysics.phy-astr.gsu.edu/hbase/pend.html http://www.acs.psu.edu/drussell/Demos/Pendulum/Pendula.html
what is the equation for a period of a pendulum