Q132 / 160 · AP EAMCET 2024 (20 May Shift 1) · Physics

A particle is executing simple harmonic motion with a time period of 3 s . At a position where the displacement of the particle is $60 \%$ of its amplitude, the ratio of the kinetic and potential energies of the particle is

A
$5: 3$
Correct answer
B
$16: 9$
C
$4: 3$
D
$25: 9$

Solution

$\mathrm{T}=3 \mathrm{~s}, \mathrm{x}=0.6 \mathrm{~A}$ $\therefore \frac{\mathrm{K} \cdot \mathrm{E}}{\mathrm{P} \cdot \mathrm{E}}=\frac{\frac{1}{2} \mathrm{~m} \omega^2\left(\mathrm{~A}^2-\mathrm{x}^2\right)}{\frac{1}{2} \mathrm{~m} \omega^2 \mathrm{x}^2}=\left(\frac{\mathrm{A}}{\mathrm{x}}\right)^2-1$ $=\left(\frac{10}{6}\right)^2-1=\frac{25-9}{9}=\frac{16}{9}$

Hence, the correct answer is option: 'B'.

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