Chapter 10, Problem 31P

Example -4s F(s) = = (s²+4)² As + B Cs+D + (s²+4) (s²+4)² (s²+4) (H.W)

The Mach number NM for flow of a perfect gas in a pipe depends upon the specific-heat ratio k (dimensionless), the pressure p, the density ρ, and the velocity V. Obtain by dimensional reasoning the form of the Mach number expression. (Buckingham pi)Answer: NM = f(V/sqrt(p/ρ), k)

oyfr 3. The figure shows a frame under the influence of an external loading made up of five forces and two moments. Use the scalar method to calculate moments. a. Write the resultant force of the external loading in Cartesian vector form. b. Determine the & direction of the resultant moment of the external loading about A. 15 cm 18 cm 2.2 N-m B 50 N 45° 10 cm 48 N.m 250 N 60 N 20 21 50 N 25 cm 100 N A 118, 27cm 5, 4:1

Assume the Link AO is the input and revolves 360°, determine a. the coordinates of limit positions of point B, b. the angles  (AOC) corresponding to the limit positions

oyfr 3. The figure shows a frame under the influence of an external loading made up of five forces and two moments. Use the scalar method to calculate moments. a. Write the resultant force of the external loading in Cartesian vector form. b. Determine the & direction of the resultant moment of the external loading about A. 15 cm 18 cm 2.2 N-m B 50 N 45° 10 cm 48 N.m 250 N 60 N 20 21 50 N 25 cm 100 N A 118, 27cm 5, 4:1

The 2-mass system shown below depicts a disk which rotates about its center and has rotational moment of inertia Jo and radius r. The angular displacement of the disk is given by 0. The spring with constant k₂ is attached to the disk at a distance from the center. The mass m has linear displacement & and is subject to an external force u. When the system is at equilibrium, the spring forces due to k₁ and k₂ are zero. Neglect gravity and aerodynamic drag in this problem. You may assume the small angle approximation which implies (i) that the springs and dampers remain in their horizontal / vertical configurations and (ii) that the linear displacement d of a point on the edge of the disk can be approximated by d≈re. Ө K2 www m 4 Cz 777777 Jo Make the following assumptions when analyzing the forces and torques: тв 2 0>0, 0>0, x> > 0, >0 Derive the differential equations of motion for this dynamic system. Start by sketching LARGE and carefully drawn free-body-diagrams for the disk and the…

A linear system is one that satisfies the principle of superposition. In other words, if an input u₁ yields the output y₁, and an input u2 yields the output y2, the system is said to be linear if a com- bination of the inputs u = u₁ + u2 yield the sum of the outputs y = y1 + y2. Using this fact, determine the output y(t) of the following linear system: given the input: P(s) = = Y(s) U(s) = s+1 s+10 u(t) = e−2+ sin(t) =e