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 evo ve on its own. Briefly describe the kind of motion the mass m will be undergoing if the air drag can be ignored. Name. You are requested to double the maximum amplitude of the motion by periodic addition of certain amount of energy,theta=1 nano-Joule with every punch) to the system. With what freauencv 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

a)here the tangential accleration a=-gsin(theta)=-g(theta)=-g(x/l)=-(g/l)x

hence acceleration is proportional to displacement from mean position

this is a simple harmoniction

b)even if the amplitude is increased to double there is no change in frequency

but the energy will be four times

hence the excitation energy E*=three times the initial energy

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