Explain why the points x = A and x = - A in Fig. 7.23b are called ?turning points.? How are the values of E and U related at a turning point?

Solution 21DQ Introduction We have discuss why the points A and -A are called turning points. The we have find out what will the relation between kinetic energy and potential energy. Step 1 As discussed in the figure, at the point A and -A the potential energy of the spring is equal to the total mechanical energy. Now the mechanical energy consists of potential energy and kinetic energy. So if the potential energy is equal to the total mechanical energy, then the kinetic energy will be zero. Hence the particle can not move further and hence the particle starts going back. That is the particle takes a u-turn at this point, that is why the point is called the turning point.