A 4-pound weight stretches a spring 2 feet. The weight is released from rest 15 inches above the equilibrium position, and the resulting motion takes place in a medium offering a damping force numerically equal to 7 8 times the instantaneous velocity. (Use g = 32 ft/s2 for the acceleration due to gravity.) Complete the Laplace transform of the differential equation. s2â„’{x} + s + sâ„’{x} + + â„’{x} = 0 Use the Laplace transform to find the equation of motion x(t).

answer: what do you mean

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4

answer: what are the following choices