Question

An SHM is represented by $x=5\sqrt{2}(sin2\pi t+cos2\pi t)$. The amplitude of the SHM is:

• A. 10 cm
• B. 20 cm
• C. $5\sqrt{2}$ cm
• D. 50 cm

Answer 1

The correct option is A 10 cm

Here, $x=5\sqrt{2}(sin2\pi t+cos2\pi t)$
$\Rightarrow x=5\sqrt{2}sin2\pi t+5\sqrt{2}cos2\pi t$ ...(i)
The standard equation of simple harmonic motion is given by
$x=A_{1}sin\omega t+A_{2}cos\omega t$ ...(ii)
Now, comparing Eqs. (i) and (ii), we obtain
$A_1=\sqrt{A_1^2+A_2^2}=\sqrt{(5\sqrt{2}{)}^2+(5\sqrt{2}{)}^2}$
$=\sqrt{50+50}$
$=10cm$