Question

The equation of a simple harmonic motion is given by $x=6sin10t+8cos10t,$ where $x$ is in cm, and t is in seconds. Find the resultant amplitude

• A. $20$
• B. $10$
• C. $30$
• D. $50$

Answer 1

Answer: (B)

$10$

Basically in

$y=A\sin \left(\omega t\right)$

A=amplitude is nothing but maximum value of y,

Same goes here too,

In $x=6\sin t+8\cos t$

Amplitude=max(x),

Which is$=\sqrt{6^2+8^2}=10$

Hence Option $\text{B}$ is the correct answer.