College Physics (4th Edition)

The correct answer is: (c) $0~s, 1~s, 7~s, 8~s$
When an object is in SHM, if the object is on the -x-side of the equilibrium point, there is a restoring force exerted on the object in the +x-direction. When the slope of the $v_x$ versus $t$ graph is positive, the acceleration is positive. That is, the acceleration is in the +x-direction. If the acceleration is in the +x-direction, then the net force is in the +x-direction. The slope of the graph is positive in the intervals $0 \leq t \lt 2$ and $6 \lt t \lt 10$ Therefore, the object is on the -x-side of the equilibrium point in the intervals $0 \leq t \lt 2$ and $6 \lt t \lt 10$ The correct answer is: (c) $0~s, 1~s, 7~s, 8~s$