JEE Main · 2023 · 01 Feb 2023 · Shift 1 · Elasticity & SHM

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The amplitude of a particle executing SHM is 3 cm. The displacement at which its kinetic energy will be 25% more than the potential energy is: ______ cm.

Answer: 2

Solution

In simple harmonic motion the potential energy at displacement

x

\frac{1}{2} m ω^{2} x^{2}

and the kinetic energy is

\frac{1}{2} m ω^{2} (A^{2} - x^{2})

. Requiring the kinetic energy to exceed the potential by a quarter,

K = \frac{5}{4} U

, gives

A^{2} - x^{2} = \frac{5}{4} x^{2} \Rightarrow A^{2} = \frac{9}{4} x^{2} \Rightarrow x = \frac{2 A}{3} .

With

A = 3 cm

, the displacement is

x = 2 cm

JEE Main · 2023 · 01 Feb 2023 · Shift 1 · Integer answer

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