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

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. (A) I, III (B) II, IV (C) II, III (D) I, IV

Tardigrade Admin · Accepted Answer

Potential energy, U =(1/2) m ω2 x 2=(1/2) m ω2 A 2 cos 2 ω t On plotting a graph between potential energy U and time t, we shall get a curve II and graph between U and x we shall get curve IV.

Q. 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.

I, III

II, IV

II, III

I, IV

Potential energy, $U = \frac{1}{2} m ω^{2} x^{2} = \frac{1}{2} m ω^{2} A^{2} cos^{2} ω t$
On plotting a graph between potential energy U and time t, we shall get a curve
II and graph between $U$ and $x$ we shall get curve IV.

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