Question

5. (16) A box weighing 16 pounds is attached to a spring with spring constant 8 1b/ft. The book is initially released from a point 2 foot above the equilibrium position with an upward velocity of 3 ft/sec (a) Set up the DE for this system. Do not solve the DE. Show your work. Write the equation in standard form. Write your answer in the box NIP 32 -IN .+ 8x=0 • levo (b) Convert the initial conditions into mathematical equations. (0) '0) = (c) Now suppose the system is immersed in a medium that offers a damping force numerically equal to 2 times the instantaneous velocity. Set up the DE for this system. Do not solve the DE. Show your work. Write the equation in standard form. (d) Now suppose that in addition to the damping force, the box is driven by an external force equal to f(t) = 3c24. Set up the DE for this system. Do not solve the DE. Show your work. Write the equation in standard form.

Answer 1

Q 16. weight = lopounds 16 = 1 kg a) mass ma K = 8 lblft ma" (t) + kalt=0 I d²x dt2 +80 x = 0 d²x dt² + 16x =0 acol = 2 alcoo=3 Taking upurand direction as positive c) now damping constant d = 2 2 dr + 2 dx + 2 da + 8 x = 0 dt dze dt² tu da 16x = 0 dt d) f(t) = 3024 malto + d alto tk x = f(t) I dx + 2x + 8x = 3e2t +16x=6e2t dar + 4 do it 272 Poole 0009