Energy In Simple Harmonic Motion

Understanding the |f_T| vs. x graph in Simple Harmonic Motion (SHM):

In SHM, the total force acting on a particle is directly proportional to the displacement from the mean position, and always directed towards the mean position:

Here, is the force constant. Taking the magnitude, we get:

This means the graph of versus is a V-shaped graph—linear on both sides of the origin, with the minimum value (zero) at and increasing symmetrically on either side as increases.

Important observations:

• At , (equilibrium position)
• As increases (either positive or negative), increases linearly
• The graph is symmetric about the origin

Thus, the correct shape of the graph is a straight V-line centered at the origin, and the correct option is (B).

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