question_answer 38)

                  The potential energy function for a particle executing linear SHM is given by \[V(x)=\,\frac{1}{2}\,k{{x}^{2}},\] where k is the force constant of the oscillator (Fig.) For k = 0.5 N/m, the graph of \[V(x)\] versus \[x\] is shown in the figure. A particle of total energy E turns back when it reaches \[x=\pm {{x}_{m}}\]. If V and K indicate the P.E. and K.E., respectively of the particle at \[x=+{{x}_{m}},\] then which of the following correct? (a) \[V=O,\]      \[K=E\] (b) \[V=E,\]      \[K=O\] (c) \[V<E,\]       \[K=O\] (d) \[V=O,\]      \[K<E\]                

Answer:

                  (b) At \[x=+{{x}_{m}}\], particle stops, so \[K=0\] and \[V=E\]