1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Fantom [35]
3 years ago
6

A 1 newton force will stretch a spring 1 meter. The spring/mass system is damped by a force that is 8 times the instantaneous ve

locity. A 16 kg mass is attached to the spring. The spring is compressed 0.6 meters above the equilibrium position and given an initial downward velocity of 2 m/s. Determine the equation of motion of the mass
Mathematics
1 answer:
sukhopar [10]3 years ago
5 0

Answer:

Step-by-step explanation:

Given the mass is m =16kg, and 1N force will stretch the spring 1 m.

That is, F =1N,Z =1m. Now find the spring constant k:

F = kL = 1 = k(1) = k= 1N/m.

The damping force is 8times the instantaneous velocity, this means β = 8,

and the external force is f(t) = 0

Initially the object compressed 0.6m above equilibrium position,

with the downward velocity is 2m/s.

The differential equation for a spring mass system with

damping force and extemal force is: mx" + βxt + kx = f(t).

so, 16x"+ 8x' + x= 0, x(0} = -0.6, x'(0)= 2m/s.

Now solve the DE:

The auxilary equation for the homogeneous equation is 16x"+8x'+x=0

solving we get, 16r² + 8r + 1 = 0 => (4r + 1)² = 0 => r = - 1/4.

Then the general solution for the homogenous system is: x(t)=c_1e^{-t/4} +c_2te^{-t\4}.

Use the initial conditions x (0) = -0.6, x'(0) = 2m/s:

x(0)=c_1e^{0} +c_2(0)e^{0}=-0.6=c_1\\x'(t)=-\frac{1}{4}c_1e^{-t/4}+c_2e^{-t/4}-\frac{1}{4}c_2te^{-t/4}\\x'(0)=-\frac{1}{4}c_1e^0+c_2e^0-\frac{1}{4}c_2(0)e^0=2=-\frac{1}{4}(-0.6)+c_2=c_2=1.85.

Hence, x(t) =-0.6e^{-t/4}+1.85te^{-t/4}.

You might be interested in
A triangle has sides with lengths of 5x -7, 3x -4, and 2x -6. What is the perimeter of the triangle?
Leokris [45]
I got 10x-17 to be the perimeter
6 0
4 years ago
When working in trigonometry, you typically measure angles in
Neporo4naja [7]

Answer:

Radians

<em>Hope that helps!</em>

Step-by-step explanation:

8 0
3 years ago
The area of the patio is 216 square feet. Write an equation that represents the area of the patio
Hoochie [10]

Answer:

216=2w \times w

Step-by-step explanation:

Assuming that the patio is a rectangle, we have

A= l\times w

Where l is the length and w is the width.

Now let's assume that the length of the patio is double than the width.

l=2w

So, the equation that represents this problem is

216=2w \times w

6 0
3 years ago
Write the equation of the line that has a slope of -4 and goes through (3,-3)
Sindrei [870]
The functional equation of the line is f (x)=a*x+b
you have already a: -4 -->f (x)=-4 x+b
Now you can use the point (3;-3)
3 is the x-coordinate and -3 the f (x)-coordinate
--> -3 = -4*(3) + b Now you can solve it
-3 = -12+b (+12)
b = 9
ANSWER: f (x) = -4x + 9
3 0
3 years ago
Which values of m and b will create a system of equations with no solution? Select two options. y = mx + b y = –2x + A system of
Nuetrik [128]

Answer:

m = -2 and b = -1/3

m = -2 and b = -2/3.

Step-by-step explanation:

y = -2x - 1/3

y = -2x - 2/3

This system has no solutions because y cannot be 2 different values at once.

5 0
3 years ago
Read 2 more answers
Other questions:
  • Help with this problem please.
    14·1 answer
  • Whats the cube root of 234
    13·2 answers
  • The heat in the house is set to keep the minimum and maximum temperatures (in degrees Fahrenheit) according to the equation |x –
    5·2 answers
  • What does y5 x y14 equal?
    13·1 answer
  • What is 2/3 times 1/12
    10·2 answers
  • Which expression is equivalent to -5(1+7x)+3(3+4x)
    8·1 answer
  • What is f(x) = x; g(x) = 1/4 x - 4 <br> (Algebra 7th Grade) <br> Please help
    12·2 answers
  • Our math class is having a field trip . The ratio of boys to girls joining the field trip is 11:4.​
    12·1 answer
  • The hypotenuse of a 30-60-90 degree triangle is 24.2 ft. What is the length of the shortest leg?
    8·2 answers
  • PLEASEE HELP.!! ILL GIVE BRAINLIEST.!! *EXTRA POINTS* DONT SKIP:((
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!