SimpleHarmonicMotion Gonzaga University（大学SimpleHarmonicMotion贡扎加）.pdfVIP

Simple Harmonic Motion 1 Object To determine the period of motion of objects that are executing simple harmonic motion and to check the theoretical prediction of such periods. 2 Apparatus Assorted weights and spheres, clamps, meter stick, spring, stand, stopwatch, protractor, string, motion detector and interfaced computer. 3 Theory Simple harmonic motion refers to a type of movement that is found in a number of apparently dissimilar situations. Three such situations will be studied in this experiment. Harmonic motion is that which repeats itself at certain intervals; one such interval is called the period of motion. A specific type of periodic motion, simple harmonic motion, has a rather straightforward mathematical representation, x = A cos (ωt + δ) (1) where A is the amplitude of motion, ω is the angular frequency, t is the elapsed time, and δ is a phase factor identifying at what point in the cycle we chose t = 0. The angular frequency is related to the period through the relationship 1 2π T = = (2) f ω If an object undergoes motion as described above, the object’s velocity and acceleration as functions of time will be, v = −Aω sin (ωt + δ) a = −Aω2 cos (ωt + δ) (3) One can now see the necessary condition for an object to undergo simple harmonic motion. Notice in equation 3, that the acceleration as a function of time is proportional to A cos (ωt + δ) which is nothing other than the po