Question
Asked Oct 3, 2019
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2

2. Suppose hat themass in a mass-spring-dashpot
SYStem with m 25
With lol- 20 and
K E) Cept cos (wt- he pseudoperiosl ha
hme-varying amplitude, and the time lag of he motion
CE 10, and K 220 is Set in motion
xlo)- 41. Find the pasition function
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2. Suppose hat themass in a mass-spring-dashpot SYStem with m 25 With lol- 20 and K E) Cept cos (wt- he pseudoperiosl ha hme-varying amplitude, and the time lag of he motion CE 10, and K 220 is Set in motion xlo)- 41. Find the pasition function

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Expert Answer

Step 1

According to the given information:

m =25
k 226
c 10
x(0) 20 and x'(0)= 41
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m =25 k 226 c 10 x(0) 20 and x'(0)= 41

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Step 2

It is known that:

mx "cx'+kx = 0
hence
25x" 10x226x = 0
the characteristics equation:
25r210r226 0
btb4ac
-10t 100 22600
r
2a
50
-1 15
-10 150i
r
50
therefore the roots are:
-1+15i
-1-15i
and 2
5
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mx "cx'+kx = 0 hence 25x" 10x226x = 0 the characteristics equation: 25r210r226 0 btb4ac -10t 100 22600 r 2a 50 -1 15 -10 150i r 50 therefore the roots are: -1+15i -1-15i and 2 5

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Step 3

Hence the general s...

x()
e3 (C cos 31C, sin 3t)
thus,
-t
x')e3C,sin3 +3C, cos 31)e(C cos 31 + C, sin3t)
(C cos 3tC sin 3t)
х()-е
also,x(0)20 and x'(0) = 41
X
x(0)e' (C)
20 C
x(0)e' (3C,)e (20)41 3C, -4=|C, =15
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x() e3 (C cos 31C, sin 3t) thus, -t x')e3C,sin3 +3C, cos 31)e(C cos 31 + C, sin3t) (C cos 3tC sin 3t) х()-е also,x(0)20 and x'(0) = 41 X x(0)e' (C) 20 C x(0)e' (3C,)e (20)41 3C, -4=|C, =15

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