The wind flutter on the wing of a newly proposed jet fighter is given by the following 1st order differential equation: With the Boundary Condition: y(0) = 1 (remember this means that y = 1 when x = 0) Determine the vertical motion (y) in terms of the span (x) of the wing. The frequency of fluctuations of the wing at mach 2 is given by the non-homogenous 2nd order differential equation: With the boundary conditions: y(0) = 1 and y(1) = 0 (i.e., y = 1 when x = 0 and y = 0 when x = 1) By solving the homogenous form of this equation, complete the analysis and determine the amplitude (y) of vibration of the wing tip at mach 2. Critically evaluate wing flutter and fluctuation frequency amplitude determined by solving the two differential equations above.

Express the boundary conditions on each boundary for each problem shown below. 40 (a) 30 (c) (d) p= kx b (e) (f)

Differential Equations - Acceleration and velocity models

For the following water liquid level system, 9mi(t) is the mass flow rate input deviation to the system and the restrictions can be considered linear resistances about the equilibrium: 9mi h2 Ro R1 a) Using basic fluids principles, develop the Dynamic Equations for the deviation of the two liquid level heights from their equilibrium height as a function of the input mass flow rate, Imi-

Engineering mechanics statics

A 5-kg object is acted upon by a horizontal force P=18t [N], where t is time in seconds. The coefficient of kinetic friction is µk = 0.15. At t = 2 s, the object's velocity is 10 m/s. Determine the velocity at t = 4 s. Use the Impulse-Momentum method. Provide the free-body diagram and show all work. P

Please show working out aND explain the bukingham theorem

2. A pendulum is a mechanical system in which a mass m is attached to a massless incxtensible string of length which is in turn connected to a frictionless pivot, as shown at right. The swing angle (t) of the pendulum satisfies the second-order nonlinear differential equation d'e 22² + sin 0-0. 2sine The transformation v -- allows us to transform this equation into the separable first-order differential equa- tion (1) U + sin 0-0. sino pivot 1 v(0)' mass 77 (a) If the mass m is initally at rest at an angle of — T/6 degrees, solve the differ- ential equation (1) to find v = v(8). (b) Given that (2) de integrate both sides of this separable differential equation to find the general solution tt(0) in the form of an integral (with respect to 0). (c) Hence, write down a definite integral for the period 7' of the pendulum (that is, the time for the mass m to complete one full swing and return to its starting position. (Note: v <0 on this section because is decreasing.) (Hint: The period is…

Fluid Mechanics Problem

Problem 1: The discharge pressure (P) of a centrifugal pump shown below is a function of flow rate (Q), impeller diameter (D), fluid density (p), and impeller angular speed (12). P = f (Q. D, p. 92). Use the Buckingham pi technique to rewrite this function in terms of dimensionless parameters, 1 g (n₂). P= P(Q,D, Dimensions 2) N= 5 Q. P