Question: The displacement of a particle is given by x = 3 sin (5$\pi t)$ + 4 cos (5$\pi t$) The amplitude...

Question

The displacement of a particle is given by x = 3 sin (5 $\pi t)$ + 4 cos (5 $\pi t$ ) The amplitude of particle is

Answer 1

Standard equation : x = a sin $\omega$ t + b cos $\omega t$

$x = \sqrt{a^{2} + b^{2}}\sin\left( \omega t + \tan^{- 1}(b/a) \right)$ Given equation

$x = 3\sin(5\pi t) + 4\cos(5\pi t)$

$x = \sqrt{9 + 16}\sin\left( 5\pi t + \tan^{- 1}4/3 \right)$

$x = 5\sin(5\pi t + \tan^{- 1}(4/3))$

Question: The displacement of a particle is given by x = 3 sin (5\(\pi t)\) + 4 cos (5\(\pi t\)) The amplitude...