Question

The potential energy function for a particle executing linear SHM is given by $\mathrm { k } = 0.5 \mathrm { Nm } ^ { - 1 }$, the graph of V(x) versus x is shown in the figure. A particle of total energy E turns back when it reaches . If V and K indicate the potential energy and kinetic energy, respectively of the particle at then which of the following is correct?

• A. V = 0, K = E
• B. V = E, K = 0
• C. V < E, K = 0
• D. V = 0,K< E

Answer 1

Answer: (B)

V = E, K = 0

Answer 2

At any instant, the total energy of an oscillator is the sum of kinetic energy and potential energy

Total energy E = K+ V

At x = the particle turns back, therefore its velocity at this point is zero, i.e. v = 0

$\therefore \mathrm { K } = 0$

$\therefore \mathrm { E } = \frac { 1 } { 2 } \mathrm { kx } ^ { 2 } = \mathrm { v }$