Question

If the speed $\left(v\right)$ of the bob in a simple pendulum is plotted against the tangential acceleration $\left(a\right)$, the correct graph will be represented by.

• A. I
• B. II
• C. III
• D. IV

Answer 1

The correct option is A I

The pendulum bob executes a simple harmonic motion. (Position is sinusoidal)

Let us assume the position with respect to the equilibrium state to be

$x=A$ $\text{sin}(\omega t+\varphi )$.

Thus, velocity is given by $v=\frac{dx}{dt}=A\omega$ $\text{cos}(\omega t+\varphi )$.

Similarly, acceleration is given by $a=\frac{dv}{dt}=-A{\omega }^2$ $\text{sin}(\omega t+\varphi )$

Observe that $(\frac{a}{A{\omega }^2}{)}^2+(\frac{v}{A\omega }{)}^2=1$

Clearly, $a-v$ curve is an Ellipse.