A string is acting as a simple pendulum that is 0.75m in length with a mass of 0

Question

A string is acting as a simple pendulum that is 0.75m in length with a
mass of 0.45kg attached to the free end. The mass is pulled to one side through a
small angle and released from rest.

1) Find the angular frequency and period of the pendulum? If the mass were
doubled, to 0.80kg, what would be the new angular frequency and period?

2) Calculate the time it would take for the mass to reach its greatest speed? Why?

3) Supposed this pendulum were placed on the moon, would its period be greater or less than on the earth given that gmoon = 1.67m/s? Why?

Explanation / Answer

T ˜ 2pv(L/g) = 2(3.14)v(0.75)/(9.8) = 1.74s f = 1/T = 1/(1.74) = 0.575Hz Period and frequency are independent of weight. Greatest speed is achieved at the bottom of its swing. This occurs at t=T/4 t = T/4 = (1.74)/4 = 0.435s T ˜ 2pv(L/g) = 2(3.14)v(0.75)/(1.67) = 4.21s Since acceleration is less, velocity is less, and the time taken to travel the same distance (one swing back and forth) will be greater.

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