The mass hanging on the end of this spring is in its rest or equilibrium position. In this equilibrium position the downward force of gravity is balanced by the upward force of the spring. The force of gravity or weight is always the same. As the mass is pulled downward, the upward force of the spring becomes greater than the downward force of the mass. This causes a net upward force. When the mass passes through its equilibrium position, the two vectors cancel out, leaving no net force acting on the mass. The mass has stopped moving at the highest position of its motion. At this point there is a net downward force. Recall Newton's second law, F equals m-a. At this position the mass experiences a net upward force, which results in acceleration upwards. As this is position with the greatest upward force, this is the point of maximum upward acceleration. When there is no net force on the mass, it has no acceleration. The velocity is at its maximum here. Here there is a net downward force and the mass is accelerated downward. The velocity is zero. This is simple harmonic motion. 1. The acceleration is always directed toward the rest position. 2. The acceleration increases as the mass moves away from the rest position. Hooke's law, F equals negative-k-x, describes the force exerted by a spring. The negative sign indicates that the force is directed opposite the direction of motion. The spring constant is k and the distance from the rest point is x. When the mass is at the lowest point in its oscillation cycle, two forces act on it, an upward force, F equals k-x, and a downward force, F equals m-g. The difference between the forces is the net force, kx - m-g. Here the the spring force, k-x, is greater than the gravitational force, m-g. Here the net force is m-a, and it causes upwards acceleration. At the top position, the spring force, k-x, is smaller than the gravitational force, m-g. The difference is the force minus m-a, which causes the mass to accelerate downward. If the spring is stretched 15 centimeters by a 45 gram mass, what is the spring constant, k, of the spring? Unit analysis will show that all the units cancel except Newtons over meters Did you use meters and kilograms? Note that the two vectors in the diagram have the same length, or magnitude. Therefore, the first step in working the problem is to write F-up equals F-down. Please check that you have written your solution in a formal manner, as shown. If you wish to receive full credit, your solution must show the concept, F-up equals F-down, the steps you took in solving the problem, and the answer expressed with correct units and with the correct number of significant figures.

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