Question 106: Oscillations

Question

A particle executes S.H.M., the graph of velocity as a function of displacement is :

Accepted Answer

For a body performing SHM, relation between velocity and displacement
$$v = \omega \sqrt {{A^2} - {x^2}} $$
now, square both side
$${v^2} = {w^2}({A^2} - {x^2})$$
$$ \Rightarrow {v^2} = {w^2}{A^2} - {\omega ^2}{x^2}$$
$${v^2} + {\omega ^2}{x^2} = {\omega ^2}{A^2}$$
divide whole equation by $${{\omega ^2}{A^2}}$$
$${{{v^2}} \over {{\omega ^2}{A^2}}} + {{{\omega ^2}{x^2}} \over {{\omega ^2}{A^2}}} = {{{\omega ^2}{x^2}} \over {{\omega ^2}{A^2}}}$$
$${{{v^2}} \over {{{(\omega A)}^2}}} + {{{x^2}} \over {{{(A)}^2}}} = 1$$
above equation is similar as standard equation of ellipses, so graph between velocity and displacement will be ellipses.

Answer

a parabola

Answer

a helix

Answer

an ellipse

Answer

a circle

Oscillations

A particle executes S.H.M., the graph of velocity as a function of displacement is :

Choose the correct answer: