Question

Two simple harmonic motions are represented by the equations
$Y_1=10\sin \left(3\pi t+\frac{\pi }{4}\right)$ and $Y_2=5\left(\sin 3\pi t+\sqrt{3}\cos 3\pi t\right)$
Their amplitudes are in the ratio of;

• A. 2:1
• B. 3:1
• C. 1:3
• D. 1:1

Answer 1

The correct option is D 1:1

Given, $Y_1=10sin(3\pi t+\pi /4)$ and

$Y_2=5(sin3\pi t+\sqrt{3}cos3\pi t)=5sin3\pi t+5\sqrt{3}cos3\pi t$

Amplitude of $Y_1$ is $A_1=10$ and

amplitude of $Y_2$ is $A_2=\sqrt{(5{)}^2+(5\sqrt{3}{)}^2}=\sqrt{25+75}=10$

Thus, $\frac{A_1}{A_2}=\frac{10}{10}=1:1$