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A simple approximate expression is derived for the dependence of the period of a simple pendulum on the amplitude. The approximation is more accurate than other simple relations.
Play with one or two pendulums and discover how the period of a simple pendulum depends on the length of the string, the mass of the pendulum bob, and the amplitude of the swing. It’s easy to measure the period using the photogate timer. You can vary friction and the strength of gravity.
The period T of a simple pendulum (measured in seconds) is given by the formula: (1) T = time for 10 oscillations / 10 oscillations (2) using equation (1) to solve for “g”, L is the length of the pendulum (measured in meters)
<< 1. Find the period of the pendulum. Determine the period of the pendulum using (a) the torque method and (b) the energy method.
understand nonlinear oscillations of a simple pendulum. KEY WORDS: Nonlinear pendulum; Period; Approximate formula; Taylor series expansion.
1. If you want a pendulum to have a period of 1 second, how long should the pendulum be? 2. If you take the same pendulum to the Moon, where g = 1.68m/s 2, what will be its period there?
A physical pendulum consists of a uniform rod of length d and mass m pivoted at one end. The pendulum is initially displaced to one side by a small angle θ 0 and released from rest with θ 0 <<1. Find the period of the pendulum. Determine the period of the pendulum using (a) the torque method and (b) the energy method. Figure 24.3 Oscillating rod
