An object of mass m (=5 kg) is attached to a weight-less line length L (=2 meter

Question

An object of mass m (=5 kg) is attached to a weight-less line length L (=2 meters) as shown on the right. The system is moved out o the vertical line to the initial angle theta0(=1 degree) and then let evolve on its own. Briefly describe the kind of motion the mass m will be undergoing if the air drag can be ignored. You are requested to double the maximum amplitude of the motion by periodic addition of certain amount of energy, t, (=1 nano-Joule with every punch) to the system. With what frequency and,? why? would you choose to apply this exciting energy' E* to achieve the target amplitude in as short a time as possible?

Explanation / Answer

motion of the pendulum will be simple harmonic motion

time period = 2 * pi * sqrt(L/g)

time period = 2 * pi * sqrt(2/9.8)

time period = 2.838 sec

frequency of the punch will be 1 punch in every 2.838 sec

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