Question

The equation of $SHM$ is given by
$x = 3\,sin(20)\pi t + 4 cos(20)\pi t$
where $x$ is in $cm$ and $t$ is in second. The amplitude is

• A. $7 \,cm$
• B. $4 \,cm$
• C. $5 \,cm$
• D. $3 \,cm$

Answer 1

Answer: (C)

Here, $x=3sin\,20\,\pi t+4cos\,20\,\pi t$
$=5\left[\frac{3}{5}sin\,20\,\pi t+\frac{4}{5}cos\,20\,\pi t\right]$
$=5\left[cos\theta \times sin20\,\pi t+sin\theta\times cos\,20\pi t\right]$
$=5sin\left(20\pi t+\theta\right)$,
It is a $SHM$ of amplitude $5 \,cm$.