Physics - SHM Question with Solution | TestHub

The given simple harmonic motions are $y_1=10\sin \omega t$ and $y_2=5\sin \omega t+5\cos \omega t$.

The amplitude of the first motion is $A_1=10$ cm.

The second motion can be written as the superposition of two components with a phase difference of $\frac{\pi }{2}$:

$A_2=\sqrt{5^2+5^2}=\sqrt{25+25}=\sqrt{50}=5\sqrt{2}$ cm.

The ratio of the amplitudes is:

$\frac{A_2}{A_1}=\frac{5\sqrt{2}}{10}=\frac{1}{\sqrt{2}}$

Thus, the ratio is $1:\sqrt{2}$.

Answer: $1:\sqrt{2}$