What is the equation simplified

Mathematics

1 answer:

Lilit [14]3 years ago

4 0

$\bf \cfrac{2}{7}(2s+3)\implies \stackrel{\textit{distributing}}{\cfrac{2}{7}\cdot 2s+\cfrac{2}{7}\cdot 3}\implies \cfrac{2\cdot 2}{7}s+\cfrac{2\cdot 3}{7}\implies \cfrac{4}{7}s+\cfrac{6}{7}$

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sukhopar [10]

Answer:

Step-by-step explanation:

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

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

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The differential equation for a spring mass system with

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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:

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