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Question

The total energy of particle executive SHM is $$80 \,J$$. What is the kinetic energy of the particle when it is at a distance of $$\dfrac{3}{4}$$ of amplitude from the mean positive?


A
45J
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B
35J
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C
55J
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D
25J
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Solution

The correct option is D $$35 \,J$$
Total energy of particle in SHM, $$U=\dfrac{1}{2}m\omega^{2}a^{2}$$

$$\dfrac{U}{E}=\dfrac{\dfrac{1}{2}m\omega^{2}y^{2}}{\dfrac{1}{2}m\omega^{2}a^{2}}=\dfrac{y^{2}}{a^{2}}\Rightarrow \dfrac{U}{80}=\dfrac{\left(\dfrac{3}{4}a\right)^{2}}{a^{2}}=\dfrac{9}{16}\Rightarrow U=45\ J$$

Physics

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