Question

Two simple harmonic motions are represented by :$y_1=10sin(4\pi t+\pi /4)$ and $y_2=5(sin4pi+\sqrt{3}cos4\pi t)$.The ration of the amplitudes of the two SHM's is:

• A. $1:1$
• B. $1:2$
• C. $2:1$
• D. $1:\sqrt{3}$

Answer 1

The correct option is A $1:1$

Amplitude of $y_1=10$

$y_2=5\sin 4\pi i+5\sqrt{3}\cos 4\pi t$

combination of two ${\perp }^r$ $($perpendicular$)$ $SHM$

$A_{rest}=\sqrt{{A_1}^2+{A_2}^2}$

$=\sqrt{25+75}=10$

Ratio is $1:1$

Hence,

option $\left(A\right)$ is correct answer.