Question 2 A spherical pendulum consists of a bob of mass m suspended from an inextensible string of length l. Determine the Lagrangian and the equations of motion. See Figure | 1.7. Note that 0, the polar angle, is measured from the positive z axis, and ø, the azimuthal angle, is measured from the x axis in the x - y plane.? V=0 Figure 1.7 A spherical pendulum. E

find u(x,y) , v(x,y) where f(z)=u+iv for function f(z)=Z2 e2z

Find the differential of the function y=x2 +2x?

Car D is constantly 3.5 feet from the center of the race track and travels at a constant speed. The angle with a terminal ray passing through Car D sweeps out r radians per second. a. How many radians 0 does the angle sweep out in t seconds? Preview b. Define a function j that determines Car D's distance to the right of the center of the race track (in feet) as a function of the number of seconds t since the start of the race. j(t) = Preview c. The angle with a terminal ray passing through Car D must sweep out 27 radians to make one full rotation, and we know it sweeps out r radians per second. How many seconds will it take Car D to complete one full lap? | seconds Preview d. Sketch the graph of the function j below.