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A particle performs simple harmonic motion with amplitude A. Its speed is tripled at the instant that it is at a distance (2A)/3 from the equilibrium position. The new amplitude of the motion is

Asked in JEE Main 2016 · v-x and a-x relations

• (1) A/3√41
• (2) 3A
• (3) A√3
• (4) (7A)/3

Step-by-step solution

Why the other options are wrong

• (1) Does not follow from A'²=x²+(v'²)/(ω²) with v'=3v.
• (2) Scales the amplitude directly with the speed, as though A∝ v at fixed x.
• (3) Comes from tripling A² instead of rebuilding it from the new speed at the same x.

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