MCQ
The potential energy function for a particle executing linear simple harmonic motion is given by $U(x)=\frac{1}{2} k x^2$, where k is the force constant of the osicllator. For $k =0.5 Nm ^{-1}$, the graph U (x) versus x is shown in the figure given below.
Image
Find out position of a particle carrying total energy 1 J moving under this potential at which it must turn back to its orignal position.
  • A
    $\pm 0.5 m$
  • B
    $\pm 1 m$
  • $\pm 2 m$
  • D
    $\pm 3 m$

Answer

Correct option: C.
$\pm 2 m$
(C) $\pm 2 m$
Since paticle is at turning point, K = 0 therefore E = 1 = U = (1/2)k x2
putting $k=0.05$, we get $x^2=4$ and $x=+2$ and $x=-2$.

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