Simple Harmonic Motion 1 Question 4

4. For a simple pendulum, a graph is plotted between its Kinetic Energy (KE) and Potential Energy (PE) against its displacement d. Which one of the following represents these correctly? (graphs are schematic and not drawn to scale)

(2015 Main)

(a)

(c)

(b)

(d)

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Answer:

Correct Answer: 4. (a)

Solution:

  1. Taking minimum potential energy at mean position to be zero, the expression of KE and PE are

KE=12mω2(A2d2) and PE=12mω2d2

Both graphs are parabola. At d=0, the mean position,

PE=0 and KE=12mω2A2= maximum

At d=±A, the extreme positions,

KE=0 and PE=12mω2A2= maximum

Therefore, the correct graph is (a).



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