## Time and Pendulum

 The expression for the angular frequency (The number of swings in a given amount of time.) of a simple pendulum (Consists of a particle of mass m, attached to a frictionless pivot P by a cable of length L.) is w = (g / L)^(1/2) and depends only on the acceleration g due to gravity and the length L of the pendulum.    Galileo found this out and used the pendulum to measure time. Since the acceleration g due to gravity and the length L of the pendulum remain constant for a pendulum, w remains constant. If we invert w, we get T (Period of the pendulum) which is seconds per swing. 1 / w = T    Since w is constant, T should be constant. So, each swing of a pendulum measures the same amount of time. We can use this as a clock. First, measure the time it takes a pendulum for a swing. Second, count the swings in an event you are measuring. Third, calculate the time by multiplying swings with time per swing. This remarkable fact about the pendulum was first discovered by Galileo Galilee.