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  • A simple harmonic motion is represented by <img alt="y=7(\sin 4 \pi n t+\sqrt{3} \cos 4 \pi n t)" src="https://entrancecorner.oncodecogs.com/gif.latex?y%3D7%28%5Csin%

A simple harmonic motion is represented by y=7(\sin 4 \pi n t+\sqrt{3} \cos 4 \pi n t) The amplitude and time period of the motion

Option: 1

1/3 Sec


Option: 2

1/4 Sec


Option: 3

1/2 Sec


Option: 4

1/6 Sec


Answers (1)

best_answer

y=7 \sin (4 \pi t)+7 \sqrt{3} \cos 4 \pi t \\

y=7 \sin (4 \pi t)+7 \sqrt{3} \sin \left(4 \pi t+\frac{\pi}{2}\right)

\sqrt{7^2+(7 \sqrt{3})^2}=\sqrt{49+147}=\sqrt{196} \\

=14 cm

w=4 \pi \not t \\

w=4 \pi \quad\left[\because \omega=\frac{2 \pi}{T}\right] \\

4 \not \pi=\frac{2 \not \pi}{T}

 4T=2 

T=\frac{2}{4} \\

T=\frac{1}{2} \text { sec }

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mansi

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