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olasank [31]
2 years ago
15

Write the slope and y-intercept of each equation.

Mathematics
1 answer:
ioda2 years ago
3 0

Answer:

okay here goes.

Step-by-step explanation:

1. slope = -5  and y-intercept is (0,6)

2. slope = 3 and  y-intercept is (0,-2)

3. -2 and (0,-4)

4. 8 and (0,1)

5. 5 and (0,-3)

6. -3 and (0,-9)

7. 7 and (0,2)

8. -1 and (0,6)

9. -4 and (0,7)

10. -6 and (0,-8)

11. 8 and (0,-5)

12. 9 and (0,3)

You owe me. That took a long time to write.

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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:

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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}.

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