For a particle executing simple harmonic motion, the displacement x is given by x=`Acosomegat`. Identify the graph, which represents the variation of potential energy (U) as a function of time t and displacement x.

Options

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

Answer

B

Explanation

(i) For the particle, `x=A "cos" omega t` i.e. it starts from the extreme position.
Its `P.E. =(1)/(2)m omega^(2)x^(2)=(1)/(2)m omega^(2)(A^(2)"cos"^(2) omega t)`
We will consider its P.E. as a function of time
At time `t=0, P.E. =(1)/(2)m omega^(2)A^(2)`
This is maximum P.E.
`therefore` The correct graph is (1).
(ii) `P.E. =(1)/(2)m omega^(2)x^(2)`
We will consider its P.E. as a function of x.
At x=0, P.E. =0 and at `x= +- A`, P.E. is maximum .
This is shown in graph (III).
Thus the correct choice is (b) I, III.