Question

At what displacement the energy is half kinetic and half potential

Answer 1

Answer:

At what displacement from the mean position its energy is half kinetic and half potential. when Kinetic energy is maximum potential energy is zero. when kinetic energy is half of its maximum, potential energy will become other half and both are equal.

Answer 2

Displacement when energy is half kinetic and half potential is $\dfrac{A}{\sqrt 2}$ .

Assuming this question is form SHM .

We know , K.E in SHM is given by :

$K.E=\dfrac{m\omega^2(A^2-x^2)}{2}$

Also , $P.E=\dfrac{m\omega^2x^2}{2}$

Here , A is amplitude, $\omega$ is angular frequency and x is displacement form mean position .

Now ,

$K.E=P.E$

$\dfrac{m\omega^2(A^2-x^2)}{2}=\dfrac{m\omega^2x^2}{2}\\\\x=\dfrac{A}{\sqrt 2}$

Hence , this is the required solution .

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