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In a simple harmonic motion, when the displacement is one-half the amplitude, what fraction of the total energy is kinetic?

Asked in CBSE AIPMT 1995 · Kinetic, potential and total energy

• (1) 1/2
• (2) 3/4
• (3) zero
• (4) 1/4

Step-by-step solution

Why the other options are wrong

• (1) comes from taking the energy split to follow the displacement split; the shares go as (x/A)², so at x=A/2 the potential share is a quarter, not a half
• (3) comes from the kinetic energy vanishes only at the extremes, where x=± A
• (4) 1/4 is the *potential* share at x=A/2; the kinetic share is what is left over

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