Question

at any instant of time the displacement of particle executing shm is half of its amplitude what fraction of total energy is kinetic and what fraction is potential energy ​

Answer 1

The fraction E/4 is potential energy and (3/4).E is  kinetic energy.

Explanation:

The total energy is given as

E = P.E + K.E = (1/2)kA^2

Now,

P.E = (1/2)kx^2

Here

x = A/2

Thus

P.E = (1/2)k.(A/2)^2   = (1/8)kA^2

P.E = (1/4).[(1/2)kA^2]

P.E = E/4

And kinetic energy

K.E = E - P.E = E - E/4

K.E = (3/4).E

Thus the fraction E/4 is potential energy and (3/4).E is  kinetic energy.

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An object of mass 40 kg is raised to a height of 5 m above the ground if the object is allowed to fall find its kinetic energy when it is Halfway down​ ?

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