A step-index Fiber has a core index of refraction = 1:25. The cut-off angle for light entering the Fiber from air is found to be 8.50º.- (1) What is the numerical aperture of the Fiber? (2) If the Fiber were submersed in water witi same NA, what would be the cut-off angle when nwater = 1.33. (3) Find the power of the Fiber after (2) km, when te power losses is (1.5) dB/km.

A uniform Simply-supported beam is found to vibrate in its first mode with the amplitude of 12 mm at its center. Assume E=200 GPa, I = 1000 mm“ , p=7500 kg/m², A=50mm² and L=2 m. Determine the maximum bending moment in the beam. Also find the first three natural frequencies.

Find the area of the region that is bounded by the given curve and lies in the specified sector. r = 3 sin(0) + 3 cos(9), 9π

where is it demonstrated that the Hamiltonian circuit's tour length is, at most, 4/3 times that of the ideal TSP trip.

19. For the network of Fig. 6.82 D, find: a. The voltage V. b. The current /2. c. The current I,. d. The power to the 12 kQ resistor. 12 kΩ 18 kN 48 V Is + v - 3 kN 12

2. calculates the trajectory r(t) and stores the coordinates for time steps At as a nested list trajectory that contains [[xe, ye, ze], [x1, y1, z1], [x2, y2, z2], ...]. Start from time t = 0 and use a time step At = 0.01; the last data point in the trajectory should be the time when the oscillator "hits the ground", i.e., when z(t) ≤ 0; 3. stores the time for hitting the ground (i.e., the first time t when z(t) ≤ 0) in the variable t_contact and the corresponding positions in the variables x_contact, y_contact, and z_contact. Print t_contact = 1.430 X_contact = 0.755 y contact = -0.380 z_contact = (Output floating point numbers with 3 decimals using format (), e.g., "t_contact = {:.3f}" .format(t_contact).) The partial example output above is for ze = 10. 4. calculates the average x- and y-coordinates 1 y = Yi N where the x, y, are the x(t), y(t) in the trajectory and N is the number of data points that you calculated. Store the result as a list in the variable center = [x_avg, y_avg]…