Question 6: Derive equations for the K.E and P.E of a body a body of mass m executing S.H.M.
Answer
P.E of mass m executing S.M.H
Consider a body of mass ‘m’ attached with a spring of spring constant ‘k’ as shown in the figure. When the body is at rest at point ‘O’, no force acts on it. Fi = 0.
Let the spring is compressed to point ‘A’ by a force Ff such that OA = x0. Then Ff = kx0.
Now the average force is,
Average work done, W = Fd, is given by
This work is stored in the spring as potential energy. Therefore,
At any point, however,
K.E of mass m executing S.H.M
Similarly, the velocity in case of SHM at any displacement is,
Therefore,
Now , putting the above value,
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