A simple pendulum is made from a string that is 0.65m inlength with a mass of 0.

Question

A simple pendulum is made from a string that is 0.65m inlength with a mass of 0.2kg attached to the free end. The mass ispulled to one side through a small angle and released fromrest. A) What is the angular frequency and period of the pendulum?If the mass were doubled, to 0.4kg, what would be the new angularfrequency and period? B) How long would it take for the mass to reach its greatestspeed? Why? C) If this pendulum were placed on the moon, would its periodbe greater or less than on the earth? Why? A simple pendulum is made from a string that is 0.65m inlength with a mass of 0.2kg attached to the free end. The mass ispulled to one side through a small angle and released fromrest. A) What is the angular frequency and period of the pendulum?If the mass were doubled, to 0.4kg, what would be the new angularfrequency and period? B) How long would it take for the mass to reach its greatestspeed? Why? C) If this pendulum were placed on the moon, would its periodbe greater or less than on the earth? Why?

Explanation / Answer

A) Angular frequency of simple pendulum is                      = g/L                         = 9.8 / 0.65                         = 3.882 rad/s    Period T = 2 / = 6.28 / 3.882 = 1.617s If the mass wee doubled, the angular frequency and periodremains same, because they are independent of mass. B) maximum speed is reached after T/4 sec ==> t = T / 4 = 1.617 / 4 = 0.4043 s C) On moon g' = g / 6 Angular frequency of simple pendulum is                      = g/6L                         = 9.8 / 6*0.65                         = 1.585 rad/s    Period T = 2 / = 6.28 / 3.882 = 3.961s period on moon > earth.

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