Question

Two SHMs are represented by the equation $y_1=10\sin \left(3\pi t+\frac{\pi }{4}\right)$ and $y_2=\left[\sin 3\pi t+\sqrt{3}\cos 3\pi t\right]$. Their amplitudes are in the ration

• A. 1:2
• B. 2:1
• C. 1:3
• D. 1:1

Answer 1

The correct option is D 1:1

Given,

$y_1=10sin(3\pi t+\pi /4)$

$y_2=5[sin3\pi t+\sqrt{3}cos3\pi t]$

$y_2=10[1/2sin3\pi t+\sqrt{3}/2cos3\pi t]$

$y_2=10\left[\right(cos\pi /3)sin3\pi t+(sin\pi /3\left)cos3\pi t\right]=10sin(3\pi t+\pi /3)$

from the above equation, $a_1=10a_2=10$

ratio $\frac{a_1}{a_2}=\frac{10}{10}$

$a_1:a_2=1:1$

The correct option is D.