A particle starts simple harmonic motion from the mean position. Its amplitude is a and total energy E. At one instant its kinetic energy is

Q: A particle starts simple harmonic motion from the mean position. Its amplitude is $a$ and total energy $E$. At one instant its kinetic energy is $3E/4.$ Its displacement at that instant is

b (b) $\frac{K}{E} = \frac{{\frac{1}{2}m{\omega ^2}({a^2} - {y^2})}}{{\frac{1}{2}m{\omega ^2}{a^2}}}$ $= \frac{{{a^2} - {y^2}}}{{{a^2}}} $ $= 1 - \frac{{{y^2}}}{{{a^2}}}$ So, $\frac{{\left( {\frac{{3E}}{4}} \right)}}{E} = 1 - \frac{{{y^2}}}{{{a^2}}}$ $\Rightarrow \frac{{{y^2}}}{{{a^2}}} = 1 - \frac{3}{4} = \frac{1}{4}$ $ \Rightarrow y = \frac{a}{2}$.

SECTION - A [PHYSICS - MCQ]

GSEB - English Medium

A particle starts simple harmonic motion from the mean position. Its amplitude is $a$ and total energy $E$. At one instant its kinetic energy is $3E/4.$ Its displacement at that instant is

A${y}={a}$
B$y=\frac{a}{2}$
C$y=\frac{a \sqrt{3}}{2}$
D$y=\frac{a}{\sqrt{2}}$

JEE MAIN 2021, Medium

STD 11 Science
NEET
STD 11 - 13. oscillations
Physics

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