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Mekhanik [1.2K]

1 year ago

8

3) There are 16 cups in a gallon. The equation c=16g gives the number of cups in terms of the number of gallons. Write another e

quation for this situation, giving the number of gallons in terms of the number of cups:

1 answer:

suter [353]1 year ago

3 0

We know the equation

$c=16g$

gives the number of cups if we know the numbe rog gallons.

If we want an equation that gives the number of gallons if we know the number of cups we just have to solve hte equation for g, that is:

$g=\frac{c}{16}$

Therefore, the equation we are looking for is:

$g=\frac{c}{16}$

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Answer:

Option C, Multiply 5/7 by 3

Step-by-step explanation:

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5/7 * 3/1

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A mass weighing 16 pounds stretches a spring (8/3) feet. The mass is initially released from rest from a point 2 feet below the

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Answer with Step-by-step explanation:

Let a mass weighing 16 pounds stretches a spring $\frac{8}{3}$ feet.

Mass= $m=\frac{W}{g}$

Mass= $m=\frac{16}{32}$

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Mass,m= $\frac{1}{2}$ Slug

By hook's law

$w=kx$

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$k=\frac{16\times 3}{8}=6 lb/ft$

$f(t)=10cos(3t)$

A damping force is numerically equal to 1/2 the instantaneous velocity

$\beta=\frac{1}{2}$

Equation of motion :

$m\frac{d^2x}{dt^2}=-kx-\beta \frac{dx}{dt}+f(t)$

Using this equation

$\frac{1}{2}\frac{d^2x}{dt^2}=-6x-\frac{1}{2}\frac{dx}{dt}+10cos(3t)$

$\frac{1}{2}\frac{d^2x}{dt^2}+\frac{1}{2}\frac{dx}{dt}+6x=10cos(3t)$

$\frac{d^2x}{dt^2}+\frac{dx}{dt}+12x=20cos(3t)$

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$m^2+m+12=0$

$m=\frac{-1\pm\sqrt{1-4(1)(12)}}{2}$

$m=\frac{-1\pmi\sqrt{47}}{2}$

$m_1=\frac{-1+i\sqrt{47}}{2}$

$m_2=\frac{-1-i\sqrt{47}}{2}$

Complementary function

$e^{\frac{-t}{2}}(c_1cos\frac{\sqrt{47}}{2}+c_2sin\frac{\sqrt{47}}{2})$

To find the particular solution using undetermined coefficient method

$x_p(t)=Acos(3t)+Bsin(3t)$

$x'_p(t)=-3Asin(3t)+3Bcos(3t)$

$x''_p(t)=-9Acos(3t)-9sin(3t)$

This solution satisfied the equation therefore, substitute the values in the differential equation

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Substitute the value of B in any equation

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Now, the general solution

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