Question

A particle executing simple harmonic motion completes $1200oscillationsperminute$ and passes through the mean position with a velocity of $3.14m{s}^{-1}.$ Determine the maximum displacement of the particle from its mean position . Also obtain the displacement equation of the particle if it particle if its displacement be zero at the instant $t=0.$

Answer 1

^{it is given that,}

^frequency,

^{$f=\frac{noofoscillation}{time}$}

^{$f=\frac{1200}{60}=20Hz$}

^{angular frequency $\omega =2\pi f=40\pi$}

^{$\because v=r\omega$}

^{$r=\frac{v}{r}=\frac{31.4}{40\pi }=0.25m$}

So, the maximum displacement is $0.25m$

Equation at t = 0

$y=a\sin \omega t$

$y=0.25\sin \left(40\pi t\right)$