A mass weighing 9 lb stretches a spring 1.5 in. The mass is displaced 5 inch in the downward direction from its equilibrium position and released with no initial velocity. Assuming that there is no damping, and that the mass is acted on by an external force of 5 cos(6t) lb, solve the initial value problem describing the motion of the mass. For this problem, please remember to use English units: ft, lb, sec.

Answers

Answer 1

Answer:

[tex]9u" + 2304u = 160cos(6t)[/tex]

[tex]u(0) = \frac{5}{12}ft[/tex] and [tex]u'(0) =0[/tex]

Step-by-step explanation:

Given

[tex]w =9lb[/tex] --- weight

[tex]L = 1.5in[/tex] --- stretch

[tex]u(0) =5in[/tex] --- initial position

[tex]u'(0) =0[/tex] --- initial velocity

[tex]\gamma =0\ lbs/ft[/tex] --- no damping

[tex]F(t) = 5cos(6t)\ lb[/tex] -- External force

Required

Solve the initial value problem

The initial value problem is calculated using:

[tex]mu" + ku = F(t)[/tex]

First, convert all lengths to ft

[tex]L = 1.5in[/tex]

[tex]L = \frac{1.5}{12}ft[/tex]

[tex]L = \frac{1}{8}ft[/tex]

[tex]u(0) =5in[/tex]

[tex]u(0) = \frac{5}{12}ft[/tex]

Weight is calculated as:

[tex]w = mg[/tex] and [tex]w = kL[/tex]

Where

[tex]g = 32fts^{-1}[/tex]

Make m the subject in [tex]w = mg[/tex]

[tex]m = \frac{w}{g}[/tex]

[tex]m = \frac{9}{32}[/tex]

Make k the subject in [tex]w = kL[/tex]

[tex]k = \frac{w}{L}[/tex]

[tex]k = \frac{9}{1/8}[/tex]

[tex]k = 72[/tex]

Recall that: [tex]mu" + ku = F(t)[/tex]

[tex]\frac{9}{32}u" + 72u = 5cos(6t)[/tex]

Multiply through by 32

[tex]9u" + 2304u = 160cos(6t)[/tex]

[tex]u(0) = \frac{5}{12}ft[/tex] and [tex]u'(0) =0[/tex]


Related Questions

I think of a number, add on 15 and my answer is 8​

Answers

Answer:

The number is -7

Step-by-step explanation:

x + 15 = 8

Answer:

the number is -7

Step-by-step explanation:

do the opposite( sum-number added)

8-15=-7

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Answers

Answer:

168

Step-by-step explanation:

34 + 58 + 100 = 192

360 - 192 = 168

Solve by elimination:
3x + 4y = 0
5x-3y = -58
A (6, -8)
B (-6, -8)
C (-8, 6)
D ( 8, 6)

Answers

Answer:

x=−8

y=6=

Step-by-step explanation:

3x+4y=0

5x−3y=−58

In order to solve by elimination, coefficients of one of the variables must be the same in both equations so that the variable will cancel out when one equation is subtracted from the other.

3x+4y=0,5x−3y=−58

To make 3x and 5x equal, multiply all terms on each side of the first equation by 5 and all terms on each side of the second by 3.

5×3x+5×4y=0,3×5x+3(−3)y=3(−58)

Simplify.

15x+20y=0,15x−9y=−174

Subtract 15x−9y=−174 from 15x+20y=0 by subtracting like terms on each side of the equal sign.

15x−15x+20y+9y=174

Add 15x to −15x. Terms 15x and −15x cancel out, leaving an equation with only one variable that can be solved.

20y+9y=174

Add 20y to 9y.

29y=174

Divide both sides by 29.

y=6

Substitute 6 for y in 5x−3y=−58. Because the resulting equation contains only one variable, you can solve for x directly.

5x−3×6=−58

Multiply −3 times 6.

5x−18=−58

Add 18 to both sides of the equation.

5x=−40

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x=−8

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x=−8,y=6

Coordinates are: (-8,6)

Graph:

find the value of x cubed minus 2x squared minus 7x + 5 of x=1/2-√3 ​

Answers

9514 1404 393

Answer:

  3

Step-by-step explanation:

For f(x) = x^3 -2x^2 -7x +5 and x=1/(2-√3), we have ...

  f(x) = ((x -2)x -7)x +5

and ...

  x = 1/(2-√3) = (2+√3)/(2^2 -3) = 2+√3

Then ...

  f(2+√3) = ((2 +√3 -2)(2 +√3) -7)(2 +√3) +5

  = (3+2√3 -7)(2+√3) +5

  = 2(√3 -2)(√3 +2) +5 = 2(3 -4) +5 = -2 +5

  f(1/(2 -√3)) = 3

_____

If you really mean x = (1/2) -√3, then f(x) = (42√3 -3)/8.

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X
X
X
X



D

E
D
D
D

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Answer:

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Answer:

90

Step-by-step explanation:

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a=leg 1

b=leg 2

(a*b)/2

(15*12)/2

180/2

90

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90

Step-by-step explanation:

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Answer:

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159.68

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499 -339.32=159.68

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Answer:

option 1 is correct

Step-by-step explanation:

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Have a nice day!

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Answers

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288

Step-by-step explanation:

If you didnt know a triangle has the area of a square/2

so basically what im saying is the area of that square/2 equals the area of the triangle

to find the area of the square you take 24 and square it

24^2=576

finally we divide that by 2

576/2=288

so the area of the triangle is 288

have a great day :D

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Answers

Answer:

The current or I = 12.

Step-by-step explanation:

Ohm's law requires you to divide 60 volts by 5 ohms, hence giving you 12.

A text book publisher wants to estimate the number of sentences per paragraph in a history textbook. The publisher count the number of sentences in 150 randomly selected paragraphs. The results are shown in the table. Based on the data what is the mean number of sentences per paragraph in the textbook?
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The limiting behavior of a function describes what happens to the function as x → ±∞. The degree of a polynomial and the sign of its leading coefficient dictates its limiting behavior.

Using the weighed mean, it is found that the mean number of sentences per paragraph in the textbook is given by:

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Beware of bots that would like to lead you to tiny ink pls don’t go it’s a scam
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