Question

The ratio of maximum acceleration to maximum velocity in a simple harmonic motion is $10s^{-1}$. At, $t=0$ the displacement is $5m$. What is the maximum acceleration ? The initial phase is $\frac{\pi }{4}$

• A. $500m/s^2$
• B. $500\sqrt{2}m/s^2$
• C. $750m/s^2$
• D. $750\sqrt{2}m/s^2$

Answer 1

Answer: (B)

$f_{max}=\omega a$
$v_{min}=a\omega$
$\frac{\omega a}{a\omega }=10$
$w=10$
$x=asin\left(\omega +\pi /4\right)$
at $f=0$
$5=asin\left(\pi /4\right)$
$a=5\sqrt{2}$
max acc. $=w2a$
$=100\times 5\sqrt{2}$
$=500\sqrt{2}$