3. Hour exam results Avg (ex 1&2), max grade, median grade, min grade 53- 56 C-, D-, F N: 10 57- 60 C, D+, F N: 18 61- 64 C+, D+, F N: 19 65- 68 B+, C, D N: 37 69- 72 A-, C, D- N: 52 73- 76 A-, C+, D- N: 52 77- 80 A, B, D- N: 55 81- 84 A+, B+, C- N: 39 85- 88 A+, A-, D- N: 47 89- 92 A+, A, C N: 32 93- 96 A+, A+, A- N: 22 97-100 A+, A+, A+ N: 03
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12. Springs and Simple Harmonic Motion X=0 X=A X=-A X=A ; v=0 ; a=-a max X=0 ; v=-v max ; a=0 X=-A ; v=0 ; a=a max X=0 ; v=v max ; a=0 X=A ; v=0 ; a=-a max
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16. What does moving in a circle have to do with moving back & forth in a straight line ?? R 8 7 8 7 x y x -R R 0 1 1 2 2 3 3 4 4 5 5 6 6 x = R cos = R cos ( t ) since = t
18. Simple Harmonic Motion: x(t) = [A]cos( t) v(t) = -[A ]sin( t) a(t) = -[A 2 ]cos( t) x(t) = [A]sin( t) v(t) = [A ]cos( t) a(t) = -[A 2 ]sin( t) x max = A v max = A a max = A 2 Period = T (seconds per cycle) Frequency = f = 1/T (cycles per second) Angular frequency = = 2 f = 2 /T For spring: 2 = k/m OR
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Hinweis der Redaktion
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Example: Given m,k and A and x(0), choose x(t), v(t), a(t), Calculate v_max and a_max, period, energy, K, U
Example: Given m,k and A and x(0), choose x(t), v(t), a(t), Calculate v_max and a_max, period, energy, K, U
Example: Given m,k and A and x(0), choose x(t), v(t), a(t), Calculate v_max and a_max, period, energy, K, U
Example: Given m,k and A and x(0), choose x(t), v(t), a(t), Calculate v_max and a_max, period, energy, K, U