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|](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5725dda6-be91-4820-9077-490102421a2d%2F3dac5d9a-facd-4025-911f-37572dc5b458%2Fft87uq_processed.jpeg&w=3840&q=75)
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|

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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