What is the displacement of a body in SHM whe | vedclass

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Question

(A) Let $U$ be the potential energy and $K$ be the kinetic energy of a body in $SHM$.Given that $U = 3K$.The potential energy in $SHM$ is given by $U

Vedclass · Accepted Answer

$x = \pm \frac{\sqrt{3}}{2} A$

Vedclass · Answer

(A) Let $U$ be the potential energy and $K$ be the kinetic energy of a body in $SHM$.Given that $U = 3K$.The potential energy in $SHM$ is given by $U = \frac{1}{2} k x^2$ and kinetic energy is $K = \frac{1}{2} k (A^2 - x^2)$,where $A$ is the amplitude and $x$ is the displacement.Substituting these into the given condition:$\frac{1}{2} k x^2 = 3 	imes \frac{1}{2} k (A^2 - x^2)$$x^2 = 3(A^2 - x^2)$$x^2 = 3A^2 - 3x^2$$4x^2 = 3A^2$$x^2 = \frac{3}{4} A^2$$x = \pm \frac{\sqrt{3}}{2} A$

What is the displacement of a body in $SHM$ when the potential energy becomes three times its kinetic energy?

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