Question

when the displacement of a mass on a spring is 1/2A, what fraction of the mechanical energy is kinetic energy and what fraction is potential energy?

Answer 1

Let the spring constant for the spring = k

Total mechanical energy= 0.5 kA^2 ...(i)

Applying conservation of mechanical energy

Total mechanical energy = kinetic energy + potential energy

0.5 k A^2= kinetic energy + 0.5 k (0.5A)^2

Kinetic energy= 0.5 k A^2(1- 0.5^2) = 0.75* (0.5 k A^2) ...(ii)

Now from (i) and (ii)

Kinetic energy = (3/4) total mechanical energy

Now,

potential energy at that point= 0.5k(0.5A)^2= 0.25 (0.5kA^2) ...(iii)

From( i) and (iii)

Potential energy = (1/4) total mechanical energy

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