Warning: Trying to access array offset on value of type bool in /home/topgsnkq/timelyhomework.com/wp-content/themes/enfold/framework/php/function-set-avia-frontend.php on line 570

Applied Mathmatics

Consider the frictionless rod, i.e. β=0. The equation of motion becomesm (d^2 r)/(dt^2 )-mω^2 r=-mg sin⁡(ωt)with g=9.81 m/s^2 and a constant angular speed ω.The rod is initially horizontal, and the initial conditions for the bead are r(0)=r_0 and r^′ (0)=v_0.A)Analytically solve this initial value problem for r(t) B)Consider the initial position to be zero, i.e. r_0=0. Find the initial velocity, v_0, that results in a solution, r(t), which displays simple harmonic motion, i.e. a solution that does not tend toward infinity. C)Explain why any initial velocity besides the one you found in part B) causes the bead to fly off the rod. D)Given r(t) displays simple harmonic motion, i.e. part B), find the minimum required length of the rod, L, as a function of the angular speed, ω. E)Suppose ω=2, graph the solutions, r(t), for the initial conditions given here: r_0=0 and initial velocities of v_0=2.40, 2.45, 2.50, and the initial velocity you found in part B). Use 0≤t≤5

 
"Looking for a Similar Assignment? Order now and Get 10% Discount! Use Code "GET10" in your order"

If this is not the paper you were searching for, you can order your 100% plagiarism free, professional written paper now!

Order Now Just Browsing

All of our assignments are originally produced, unique, and free of plagiarism.

Free Revisions Plagiarism Free 24x7 Support