For a particle executing SHM, the displacement $x$ is given by $x = A \cos ω t$ . Identify the graph which represents the variation of potential energy (PE) as a function of time $t$ and displacement $x$ .

Question

TestHub · Accepted Answer

Potential energy as a function of displacement :

$P E = \frac{1}{2} k y^{2}$

$\Rightarrow$ PE vs y graph will be an upwards parabola.

$\Rightarrow$ $graph III$

Potential energy as a function of time:

$P E = \frac{1}{2} k y^{2} = \frac{1}{2} k {(A \cos^{2} ω t)}^{2}$

$\Rightarrow P E = \frac{1}{2} k A^{2} \cos^{2} ω t = \frac{1}{2} k A^{2} \frac{(1 + \cos 2 ω t)}{2}$

$\Rightarrow$ PE vs time is a cosine wave with angular frequency $2 ω \Rightarrow g r a p h I .$

Physics - SHM Question with Solution | TestHub

Options:

Doubts & Discussion