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  • The equation of a particle executing a  simple harmonic motion is given by <img alt="x= sin \Pi (t+\frac{1}{6})m" src="https://entrancecorner.oncodecogs.com/gif.latex?x%3D%20sin%20%5CPi%2

The equation of a particle executing a  simple harmonic motion is given by x= sin \Pi (t+\frac{1}{6})m. At t= 1 sec, the speed of the particle is?

Option: 1

272 m/s


Option: 2

274 m/s


Option: 3

277 m/s


Option: 4

300 m/s


Answers (1)

best_answer

\begin{aligned} & x=\sin \pi\left(t+\frac{1}{6}\right) \\ & v=\frac{d x}{d t}=\pi \operatorname{cos} \pi\left(t+\frac{1}{6}\right) \\ & \text { At } t=1 \sec \quad V=\pi \cos \pi\left(1+\frac{1}{6}\right) \\ & \text { or } v=\Pi \cos \left(\pi+\frac{\pi}{6}\right) \end{aligned}

\begin{aligned} & V=-\pi \cos \frac{\pi}{6}=-\pi \times \frac{\sqrt{3}}{2} \\ & V=\frac{-3.14 \times 1.732}{2}=\frac{5.44}{2} \\ & V=2.72 \mathrm{~m} / \mathrm{s} \\ & \text { or } V=272 \mathrm{~cm} / \mathrm{s} \end{aligned}

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Irshad Anwar

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