Question

Displacement - time equation of a particle is given as $x=Asin(t+\frac{\pi }{6})-Acos(t+\frac{\pi }{6})$

• A. the motion of the particle is not simple harmonic
• B. at $t=0$ , acceletation of particle is positive
• C. at $t=0$ velocity of particle is negative
• D. none of these

Answer 1

The correct option is B at $t=0$ , acceletation of particle is positive

The motion is simple harmonic because of sinusoidal dependence.
$Att=0;x=Asin\left(\frac{\pi }{6}\right)-Acos\left(\frac{\pi }{6}\right)$
$=\frac{A}{2}-\frac{A\times \sqrt{3}}{2}$
$=\frac{A}{2}(1-\sqrt{3})$
$a=-{\omega }^{2}x$
at t$=0$ $x$ is -ve. Thus $a$ is +ve
$V=\frac{dx}{dt}=Acos(t+\frac{\pi }{6})+Asin(t+\frac{\pi }{6})$
Velocity is positive