4. (5 pts) Find the equation of motion in the form x()-Acos(ot -5) for a sprin and system by esti...
PROBLEM 5 Starting with the integral equation of motion, Ot derive the differential form of the equation. Hint: To do this, look at how we derived the differential form of the mass continuity equation. There are parallels, although thisis more complicated. Note that youil ave to apply the gradien identt. fHp di -
Show that the relativistic equation ot motion can be written in the form (V.f) Mo dv 1-(v/c)]' Y2 dt point charge, and that i t is the Lorent2 torce on a qlE+ VxB), the right-hand side becomes 9E+VxB- Iv. E) /c 1 v Show that the relativistic equation ot motion can be written in the form (V.f) Mo dv 1-(v/c)]' Y2 dt point charge, and that i t is the Lorent2 torce on a qlE+ VxB), the right-hand side becomes...
5. Find the equation of motion of the system shown in Figure Q.5 assuming that the cylinder rotates without slipping. k2 X re ww m2, 10 Figure Q.5
Problem 3.(30 pts) Derive the equation of motion and find the steady state response of the system shown below for rotational motion about the hinge O for the following data: a 0.25 m, b-0.5m, m, k (You can assume that gravitational force is balanced against the static deflection of the springs) F(t) = Fo sin (ot Uniform rigid bar, mass m M.
Find a synchronous solution of the form Acos 2t+B sint to the given forced oscillator equation using the method of insertion, collecting terms, and matching coefficients to solve for A and B. y'"' + 2y' + 2y = 4 sin 3t, 2 = 3 A solution is y(t)=
Find the solution fort in the equation 5(21)=4. O t= -0.322 Ot=0.861 O t= -0.861 Ot=0.322
4. Derive the equations of motion for the shown two degrees system in terms of x and ?. Bonus 12.5 Pts: Derive and solve the characteristic equation for l = 4 m, m = 3 kg, ki-1 N/m, and k2 = 2 N/m. .
5. [25 pts total Consider the H-atom system of an electron freely moving about a nu When solve, looking at this system in spherical coordinates we obtain three differential equations to representing the radial distance (r), axial angle (θ), and azimuthal angle (d) coo rdinates. a) 12 pts] What is the approximation typically invoked to treat this system as just the behavior of the electron motion? Why is it acceptable to do so? b) [3 pts] Sketch a representation of...
3. Given the following system that is harmonically excited by x(t) = Xo sin at. Xosin(ot) a. Draw the appropriate free body diagram. (5 points) b. Write the equation of motion. (5 points) c. Solve for the natural frequency. (5 points) d. Solve for the critical damping. (5 points) e. Solve for the displacement amplitude of the rotation. (5 points)
8. (4 pts) Find the equation of the line parallel to y = -2x + 1 that passes through the point (-4,6). 9. (4 pts) Find the equation of the line that passes through the points (-2,5) and (-1,8). OS 10. Multiply and/or divide as indicated. Give your answers in fully-factored form. 6x +30 (4 pts) 18 a b. (4 pts) 20x 18y 27y5 5x c. (3 pts) x2-36 x+7 x2-49 x+6 d. (3 pts) 3b+5 10b-5 6b2+7b-5 2b-1 4