"Two simple harmonic motion, are represented by the equations ${y_1} = 10\sin \left( {3\pi t + {\pi \over 3}} \right)$ ${y_2} = 5(\sin 3\pi t + \sqrt 3 \cos 3\pi t)$ Ratio of amplitude of y1 to y2 = x : 1. The value of x is ______________."

Question

Accepted Answer

"${y_1} = 10\sin \left( {3\pi t + {\pi \over 3}} \right)$ $\Rightarrow$ Amplitude = 10

${y_2} = 5(\sin 3\pi t + \sqrt 3 \cos 3\pi t)$

$${y_2} = 10\left( {{1 \over 2}\sin 3\pi t + {{\sqrt 3 } \over 2}\cos 3\pi t} \right)$$

$${y_2} = 10\left( {\cos {\pi \over 3}\sin 3\pi t + \sin {\pi \over 3}\cos 3\pi t} \right)$$

${y_2} = 10\left( {3\pi t + {\pi \over 3}} \right)$ $\Rightarrow$ Amplitude = 10

So ratio of amplitudes = ${{10} \over {10}}$ = 1"

Two simple harmonic motion, are represented by the equations ${y_1} = 10\sin \left( {3\pi t + {\pi \over 3}} \right)$ ${y_2} = 5(\sin 3\pi t + \sqrt 3 \cos 3\pi t)$ Ratio of amplitude of y₁ to y₂ = x : 1. The value of x is ______________.

Solution

About this question

Drill 25 more like these. Every day. Free.

Two simple harmonic motion, are represented by the equations ${y_1} = 10\sin \left( {3\pi t + {\pi \over 3}} \right)$ ${y_2} = 5(\sin 3\pi t + \sqrt 3 \cos 3\pi t)$ Ratio of amplitude of y1 to y2 = x : 1. The value of x is ______________.

Solution

About this question

More Oscillations questions

Drill 25 more like these. Every day. Free.

Two simple harmonic motion, are represented by the equations ${y_1} = 10\sin \left( {3\pi t + {\pi \over 3}} \right)$ ${y_2} = 5(\sin 3\pi t + \sqrt 3 \cos 3\pi t)$ Ratio of amplitude of y₁ to y₂ = x : 1. The value of x is ______________.