MATH 4A Lecture Notes - Lecture 8: Simple Harmonic Motion
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Goal: come up with a differential equation that models the motion of a spring- mass system. Our equation will be based on newton"s second law of motion f=ma. Think about two external forces that affect the motion. Hooke"s law, the force exerted by the spring is proportional to the distance the spring is distanced or sketched. Assume that damping is due to friction between the object and the table and that it is proportional to the velocity. If the damping coefficient b>0, how do we express the damping force, A 2 kg mass is resting on a table attached to a spring: Suppose it takes a 4 n force to hold the object half a meter from the natural position of the spring. Write down the differential equation governing the motion of the system. The amplitude a and phase angle are determined by the initial conditions. Suppose 1 pull block out 0. 5 m and let it go.
