In the first problem from the activity we found that the rate of change of energy with respect to time is power. The rate of change of energy with respect to position also has physical meaning. It is the negative force. (a) The potential energy of an object oscillating on a spring stretched a distance x from equilibrium is P E = 1 2 kx2 , where k is a constant that describes the stiffness of the spring. Take the derivative with respect to time in order to find the power of the moving object. (b) Now find − d(P E) dx in order to find the force acting on the object.

In the first problem from the activity we found that the rate of change of energy with respect to time is power. The rate of change of energy with respect to position also has physical meaning. It is the negative force. (a) The potential energy of an object oscillating on a spring stretched a distance x from equilibrium is P E = 1 2 kx2 , where k is a constant that describes the stiffness of the spring. Take the derivative with respect to time in order to find the power of the moving object. (b) Now find − d(P E) dx in order to find the force acting on the object.