Question

Graph between velocity and displacement of particle, executing SHM is :

• A. a straight line
• B. a parabola
• C. a hyperbola
• D. an ellipse

Answer 1

Answer: (D)

Displacement $y=a\sin \omega t$ Velocity $v=\omega \sqrt{a^2-y^2}$ Or $v^2={\omega }^2(a^2-y^2)$ Or $\frac{v^2}{{\omega }^2}=a^2-y^2$ $\frac{v^2}{{\omega }^2{a}^2}+\frac{y^2}{a^2}=1$ This is the equation of ellipse.