Energy Graphs in SHM – Rankers Physics

Energy in SHM: Practice Problem & Solution

Assertion (A): The graph of potential energy and kinetic energy of a particle in SHM with respect to position is a parabola. Reason (R): The potential energy and kinetic energy of a particle in SHM, do not vary linearly with position.  
Both (A) & (R) are true and the (R) is the correct explanation of the (A)
Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(A) is true but (R) is false
Both (A) and (R) are false

Solution Explained:

To solve this problem, we apply the core principles of Energy in SHM. Understanding the underlying formula is key to arriving at the correct answer below:

Potential energy in SHM is \( PE = \frac{1}{2} kx^2 \), which is a parabola. Kinetic energy is \( KE = \frac{1}{2} k(A^2 - x^2) \), also a parabola. So (A) is true. Since both are quadratic functions of position \( x \), they do not vary linearly. Thus, (R) is true and correctly explains (A).

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