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Each of the equations models the damped harmonic motion of a mass on a spring a. Find the number of complete oscillations that occur during the time interval 0sts 10 seconds. b. Use a graph to determine how long it will be (to the nearest tenth of a second) until the absolute value of the displacement of the mass is always less than 0.01. f(t) = -1le 0.41 cos t

Each of the equations models the damped harmonic motion of a mass on a spring a. Find the number of complete oscillations that occur during the time interval 0sts 10 seconds. b. Use a graph to determine how long it will be (to the nearest tenth of a second) until the absolute value of the displacement of the mass is always less than 0.01. f(t) = -1le 0.41 cos t

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Need better explanation of part (B) only.

b) We need to find the smallest value of rfor which the absolute value of the displacement of the mass is always less than 0.01 Input the function Y, =- le* cos zr in graphing calculator say TI-83 and then press GRAPH key. Ploti Plotz Plot3 Y1E-11e (-0.4X) cos (TX) Y3 = Ys= Y6 = After a bit trial of trial and error in choosing an appropriate viewing window, we obtain the graph of Y, appears in window [30,70, X scz = 10]by [-0.05,0.05, Yc = 0.001]as shown below: Graph of f(t)=-1le 0d" cos zt Now use the TRACE or INTERCET feature to determine for -0.1s f(1)s0.01 Intersectionl X=17.163271 lv=.01 Therefore =17.16|
Transcribed Image Text:b) We need to find the smallest value of rfor which the absolute value of the displacement of the mass is always less than 0.01 Input the function Y, =- le* cos zr in graphing calculator say TI-83 and then press GRAPH key. Ploti Plotz Plot3 Y1E-11e (-0.4X) cos (TX) Y3 = Ys= Y6 = After a bit trial of trial and error in choosing an appropriate viewing window, we obtain the graph of Y, appears in window [30,70, X scz = 10]by [-0.05,0.05, Yc = 0.001]as shown below: Graph of f(t)=-1le 0d" cos zt Now use the TRACE or INTERCET feature to determine for -0.1s f(1)s0.01 Intersectionl X=17.163271 lv=.01 Therefore =17.16|
Each of the equations models the damped harmonic motion of a mass on a spring. s on a. Find the number of complete oscillations that occur during the time interval 0 sts 10 seconds. b. Use a graph to determine how long it will be (to the nearest tenth of a second) until the absolute value of the displacement of the mass is always less than 0.01. f(t) = -1le 0.41 cos mt
Transcribed Image Text:Each of the equations models the damped harmonic motion of a mass on a spring. s on a. Find the number of complete oscillations that occur during the time interval 0 sts 10 seconds. b. Use a graph to determine how long it will be (to the nearest tenth of a second) until the absolute value of the displacement of the mass is always less than 0.01. f(t) = -1le 0.41 cos mt
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