Question 189: Oscillations

Question

Two simple harmonic motions are represented by the equations
$${x_1} = 5\sin \left( {2\pi t + {\pi  \over 4}} \right)$$ and $${x_2} = 5\sqrt 2 (\sin 2\pi t + \cos 2\pi t)$$. The amplitude of second motion is ................ times the amplitude in first motion.

Accepted Answer

$${x_2} = 5\sqrt 2 \left( {{1 \over {\sqrt 2 }}\sin 2\pi t + {1 \over {\sqrt 2 }}\cos 2\pi t} ight)\sqrt 2 $$
$$ = 10\sin \left( {2\pi t + {\pi  \over 4}} ight)$$
$$	herefore$$ $${{{A_2}} \over {{A_1}}} = {{10} \over 5} = 2$$

Oscillations

Two simple harmonic motions are represented by the equations ${x_1} = 5\sin \left( {2\pi t + {\pi \over 4}} \right) and {x_2} = 5\sqrt 2 (\sin 2\pi t + \cos 2\pi t)$. The amplitude of second motion is ................ times the amplitude in first motion.

Integer / Numeric Answer Type