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Which graph represents the difference between total energy and potential energy of a particle executing SHM versus its distance from the mean position?

Asked in JEE Main 13th April 1st Shift 2023 · Energy graphs

• (1) an inverted parabola, maximum at x=0 and falling to zero at x=± A
• (2) a triangle, peaking at x=0 and falling linearly to zero at x=± A
• (3) a V-shape, zero at x=0 and rising to a maximum at x=± A
• (4) an upright parabola, zero at x=0 and rising to a maximum at x=± A

Step-by-step solution

Why the other options are wrong

• (2) A triangle would require K∝ A-|x|; the relation involves A²-x².
• (3) This is the potential energy itself, not the difference between total and potential energy.
• (4) The upright parabola is U; subtracting it from the constant total energy turns the curve over.

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