Question

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

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

Answer 1

Answer: (B)

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