Question

The curve between the acceleration and velocity of a particle executing SHM is a/an

• A. ellipse
• B. circle
• C. parabola
• D. straight line

Answer 1

The correct option is A ellipse

We have $x=Asin\left(\omega t\right)$
Thus, $v=dx/dt=A\omega cos\left(\omega t\right)$
Also, $a=-{\omega }^{2}x=-A{\omega }^{2}sin\left(\omega t\right)$
Thus, we have $si{n}^2\left(\omega t\right)+co{s}^2\left(\omega t\right)=1$, giving $(\frac{-a}{A{\omega }^2}{)}^2+(\frac{v}{A\omega }{)}^2=1$
or, $v^2{\omega }^2+a^2=A^2{\omega }^4=c^2$, which is the equation of an ellipse