For (a) there is a negative slope (lower dashed line) related to the Umotor = -t(theta), the coiled spring contribution, while the positive slope (upper dashed line) relates to the external load contribution. This results in an overall downward slopes. the total potential energy (equal to (w1R-t)(theta)) decreases as time increases (theta is constant).
For (b) the graph is rather similar to (a) except is related to an imperfect shaft. What can be noticed is that due to the set up of (b) the contributation by the spring follows a sine-wave like curve, which is then reflected in the total potential energy line.
From figure 10.6, figure (c) contains a 2D landscape graph, since it depends on both the angles alpha and beta. Figure 10.8 displays the landscape graph for an unloaded machine, containing both valleys and barriers. Travelling along a valley is ideal but impossible to do indefinitely, so movements over the barriers are necessary. For a loaded machine, figure 10.9 shows the landscape graph, explaining that it is simply a tilted version of figure 10.8