Question

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

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

Answer 1

Answer: (C)

Here, $x=3sin20\pi t+4cos20\pi t$
$=5\left[\frac{3}{5}sin20\pi t+\frac{4}{5}cos20\pi t\right]$
$=5\left[cos\theta \times sin20\pi t+sin\theta \times cos20\pi t\right]$
$=5sin\left(20\pi t+\theta \right)$,
It is a $SHM$ of amplitude $5cm$.