The potential energy function for a particle executing linear SHM is given by where k is the force constant of the oscillator (Figure). For k = 0.5N/m, 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 P.E. and K.E., respectively of the particle at , then which of the following is correct?
(a) V = O, K = E
(b) V = E, K = O
(c) V < E, K = O
(d) V = O, K < E.
The answer is the option (b) V = E, K = O
Potential energy at any position,
Total energy of the mass,
Kinetic energy at any position,
Now,
at extremes.
U min = 0 {x=0 at mean}
{x=0 at mean}
K min = 0 {extremes}
Hence, is constant at all times
When particle is at x = xm (mean), KE =0
So, total energy is
So, option b is correct.