Mechanical vibrations example problem 3

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Mechanical vibrations example problem 3
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Lecture By: Mr. Er. Himanshu Vasishta, Tutorials Point India Private Limited.
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TutorialsPoint_
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how u took theta dot as common as there are only 2 theta dot and 1 theta?
And when u r differentiating the potential energy, why theta is not becoming theta dot?

samratchakravarty
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What is the natural frequency of same system when if one additional spring is included to hang pulley

kinthalisantosh
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Sir ! Do we consider the change in the potential energy in the mass as 'mgx'?

sharuselva
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why is it after you take out the common teta dot become teta double dot?

nazwanshahzakaria