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  • A body oscillates with SHM according to the equation <img alt="x=7 \cos \left(3 \pi t+\frac{\pi}{4}\right)" src="https://entrancecorner.oncodecogs.com/gif.latex?x%3D7%20%5Ccos%20%5Cleft%2

A body oscillates with SHM according to the equation

x=7 \cos \left(3 \pi t+\frac{\pi}{4}\right)
Af  t=1  calculate the displacement and speed


 

Option: 1

46.7 m/s


Option: 2

35.6 m/s


Option: 3

45.8 m/s


Option: 4

32.6 m/s


Answers (1)

best_answer

\text { displacement }=(7 \mathrm{~m}) \text { cos }\left[3 \pi \times 1+\frac{\pi}{4}\right] \\
=(7 \mathrm{~m}) \cdot \cos \left(3 \pi+\frac{\pi}{4}\right) \\
=-7 \times 0.707 \\

=-4.949 \mathrm{~m} \\

\text { speed }=-(7 \mathrm{~m}) \cdot(3 \pi) \sin \left[3 \pi \times 1+\frac{\pi}{4}\right] \\

=-(7 \mathrm{~m})(3 \pi) \sin \left[3 \pi+\frac{\pi}{4}\right] \\

=21 \pi \times 0.707 \\

=21 \times 3.14 \times 0.707 \\

=21 \times 2.21998 \\

=46.7 \mathrm{~m} / \mathrm{s}

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Gaurav

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