Question

Recitation- Introducing Simple Harmonic Motion According to our textbook a mass on a spring undergoes "Simple Harmonic Motion" which means that as it bounces it obeys the position equation, y(t) = A cos(wt+). 0000000000000000 This has the following graph for p = 0. y (cm) n t(s) 1) Assume each box represents 1 cm vertically and 1 seconds horizontally. The period is defined as the amount of time required for one full cycle of motion. Measure the period using the “peak- to-peak” or “trough-to-trough” method. 2) Argue how the definition of period gives us the following relationship y(t) = y(t +T)

Answer 1

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0 From the figure, one full cycle contains 8 bones horizon izontally. each bou re represents is time period of oscillation, Thus, the T = 8x1 s - of s 2 Position equation of the cox, y (t) = A costat e f) 4 b y (t) = Acos(wt) - Again, Itt A cos [ W/t +T) A cos[wt & wt wt + 27 4TXT] costat & 2T as, A los w=21 T A From A cosent) - lii equation (i) and (ii), we get 701) +++