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Explain and draw the graphs of kinetic energy, potential energy and mechanical energy versus displacement for SHM. |
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Answer» Solution :Kinetic energy of SHM `K(x) = (1)/(2)k(A^(2)-x^(2))` Potentiall energy `U(x)= (1)/(2) KX^(2)` and Mechanical energy `E= (1)/(2) kA^(2)` The magnitude of ENERGIES at different position of SHM are shown as below :  From these values graph of energies versus displacement is obtained as below :  Following points are clear from graph : (1) `E to x` graph is linear and is parallel to displacement axis, so we can say that mechanical energy does not depends on displacement, but remains constant. (2) Shapes of `K(x) to x" and " U(x) to x` graphs are PARABOLIC. (3) At fixed point x=0, potentiall energy is zero and kinetic energy is maximum and is equal to mechanical energy. (4) As the oscillator goes towards any side increase in potentiall energy is equal to decrease in kinetic energy. (5) At extreme point `(y= |A|)`, potential energy is maximum and kinetic energy is zero. This maximum potential is equal to mechanical energy. (6) At any point of SHM path, the sum of potential and kinetic energy is equal to mechanical energy. (7) Coodinates of point of intersections of graph of kinetic energy and potential energy is `(pm (A)/(sqrt(2)), (E )/(2))`. |
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