A uniform beam of arbitrary, unsymmetrical cross-section and length 2 is built-in at one end and simply supported in the vertical direction at a point halfway along its length. This support, however, allows the beam to deflect freely in the horizontal x direction. For a vertical load W applied at the free end of the beam, calculate bending moments for the sections at A and B.

Which type of microscope would allow the viewer to see ribosomes inside a cell?

Aparticle of mass m is projected with an initial velocity v0 in a direction making an angle α with the horizontal level ground as shown in the figure. the motion of the particle occurs under a uniform gravitational field g pointing downward. (a) write down the lagrangian of the system by using the cartesian coordinates (x, y). (b) is there any cyclic coordinate(s). if so, interpret it (them) physically. (c) find the euler-lagrange equations. find at least one constant of motion. (d) solve the differential equation in part (c) and obtain x and y coordinates of the projectile as a function of time. (e) construct the hamiltonian of the system, h, and write down the hamilton’s equations (canonical equations) of motion.

However, had it been a real sound, the sound's pitch would have been increased by the doppler effect, since the falcon was moving the source of the sound. perpendicular to away from towards at the same speed as