Oscillations

JEE Main level, numerical answer, medium

83 of 194

Question 83 of 194

The amplitude of a particle executing SHM is 3cm3cm. The displacement at which its kinetic energy will be 2525% more than the potential energy is: ______ cmcm.

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Answer: 2

Let xx be the displacement at which its kinetic energy will be 2525% more than the potential energy.
Given here, A=3cmA=3cm and KE=PE+PE4KE=PE+\dfrac{PE}{4}
So, KE=54PEKE=\dfrac{5}{4}PE
⇒12mω2(A2−x2)=54×12mω2x2\Rightarrow \dfrac{1}{2}m{\omega }^{2}\left({A}^{2}-{x}^{2}\right)=\dfrac{5}{4}\times \dfrac{1}{2}m{\omega }^{2}{x}^{2}
⇒A2−x2=54x2\Rightarrow {A}^{2}-{x}^{2}=\dfrac{5}{4}{x}^{2}
⇒9x24=A2\Rightarrow \dfrac{9{x}^{2}}{4}={A}^{2}
⇒x=23A\Rightarrow x=\dfrac{2}{3}A
∴x=23×3cm∴x=\dfrac{2}{3}\times 3cm
⇒x=2cm\Rightarrow x=2cm

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