Two simple harmonic motion- are represented by the equations y1-10 sin 3- t-3 y2-5 sin 3- t-3cos3- t Ratio of amplitude ofy1 to y2-x-1-The value of x is -

For the equation nbsp; y_1=10 sin ( 3π t+π3 ) amplitude is 10 units. For the equation nbsp;y_2=5 ( sin 3π t+√(3)cos3π t ) can be simplified as nbsp; y_ ...

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Standard XII

Physics

KE & PE Graph

Two simple ha...

Question

Two simple harmonic motion, are represented by the equations $y_{1} = 10 sin (3 π t + \frac{π}{3})$

$y_{2} = 5 (sin 3 π t + \sqrt{3} cos 3 π t)$
Ratio of amplitude of

$y_{1}$ to $y_{2} = x : 1.$
The value of $x$ is _________.

1.00

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1.0

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Solution

For the equation $y_{1} = 10 sin (3 π t + \frac{π}{3})$ amplitude is $10$ units.

For the equation $y_{2} = 5 (sin 3 π t + \sqrt{3} cos 3 π t)$ can be simplified as
$y_{2} = 10 (\frac{1}{2} sin 3 π t + \frac{\sqrt{3}}{2} cos 3 π t)$
$y_{2} = 10 (cos 60 sin 3 π t + sin 60 cos 3 π t)$
$y_{2} = 10 sin (3 π t + 60)$

Amplitude in this case is $10$ units.
Hence, ratio of amplitudes is $1 : 1$
$x = 1, 1.0, 1.00$

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Two simple harmonic motion, are represented by the equations y1=10sin(3πt+π3) y2=5(sin3πt+√3cos3πt) Ratio of amplitude of y1 to y2=x:1. The value of x is _________.

For the equation y1=10sin(3πt+π3) amplitude is 10 units. For the equation y2=5(sin3πt+√3cos3πt) can be simplified as y2=10(12sin3πt+√32cos3πt) y2=10(cos60sin3πt+sin60cos3πt) y2=10sin(3πt+60) Amplitude in this case is 10 units. Hence, ratio of amplitudes is 1:1 x=1,1.0,1.00

Two simple harmonic motion, are represented by the equations $y_{1} = 10 sin (3 π t + \frac{π}{3})$

$y_{2} = 5 (sin 3 π t + \sqrt{3} cos 3 π t)$
Ratio of amplitude of

$y_{1}$ to $y_{2} = x : 1.$
The value of $x$ is _________.