Question 115: Oscillations

Question

When a particle executes SHM, the nature of graphical representation of velocity as a function of displacement is :

Accepted Answer

Since, the particle is executing SHM.
Therefore, displacement equation of wave will be
$$y = A\sin \omega t$$
$$ \Rightarrow y/A = \sin \omega t$$
and wave velocity equation will be
$${v_y} = {{dy} \over {dt}} = A\omega \cos \omega t$$
$$ \Rightarrow {v_y}/A\omega  = \cos \omega t$$
Now, $${\sin ^2}\omega t + {\cos ^2}\omega t = 1$$
$$	herefore$$ $${(y/A)^2} + {({v_y} / A\omega )^2} = 1$$
This equation is similar to the equation of ellipse.

Answer

circular

Answer

straight line

Answer

parabolic

Answer

elliptical

Oscillations

When a particle executes SHM, the nature of graphical representation of velocity as a function of displacement is :

Choose the correct answer: