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  • At a given point of time the value of displacement of a simple harmonic oscillator is given as y = A cos (30°). If amplitude is 40 cm and kinetic energy at that time is 200 J, the value of forc

At a given point of time the value of displacement of a simple harmonic oscillator is given as y = A cos (30°). If amplitude is 40 cm and kinetic energy at that time is 200 J, the value of force constant is 1.0 × 10x Nm–1. The value of x is ___________

Option: 1

4


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

best_answer

\begin{aligned} & \mathrm{v}=\omega \sqrt{\mathrm{A}^2-\mathrm{y}^2} \\ & \mathrm{y}=\mathrm{A} \times \frac{\sqrt{3}}{2} \\ & \mathrm{v}=\omega \sqrt{\mathrm{A}^2-\frac{3 \mathrm{~A}^2}{4}}=\frac{\omega \mathrm{A}}{2} \\ & \text { Given, } \mathrm{KE}=200 \mathrm{~J} \end{aligned}

\begin{aligned} & \frac{1}{2} \mathrm{~m} \frac{\omega^2 \mathrm{~A}^2}{4}=200 \\ & \mathrm{KA}^2=1600 \quad\left(\mathrm{~K}=\mathrm{m} \omega^2\right) \\ & \mathrm{K}=\frac{1600}{\left(40 \times 10^{-2}\right)^2} \\ & \mathrm{~K}=10^4 \mathrm{~N} / \mathrm{m} \\ & \mathrm{x}=4 \end{aligned}

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Suraj Bhandari

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