Question 188: Oscillations

Question

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 y
1
to y
2
= x : 1. The value of x is ______________.

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

Oscillations

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 y 1 to y 2 = x : 1. The value of x is ______________.

Integer / Numeric Answer Type