The differential equation for small-amplitude vibrations y(r, f) of a simple beam is given by a*y + E = 0 ax pA where p = beam material density A = cross-sectional area I= area moment of inertia E = Young's modulus Use only the quantities p, E, and A to nondimensionalize y, x, and t, and rewrite the differential equation in dimensionless form. Do any parameters remain? Could they be removed by further manipulation of the variables?
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- A rectangular tube of outer width w = 7.5 m, outer height h = 5 m and thickness t = 0.17 m experiences bending through the x axis. What is the moment of inertia of the cross-sectional area In? y -- X MATLAB input variables: format shortEng W = 7.5; h = 5; t = 0.17; moment of inertia I, = m4GIVE ME THE COMPLETE SOLUTION FOR THISTHIS IS THE ANSWER ACC TO THE ANSWER KEY I JUST NEED HELP FOR THE SOLUTION Theta3/T = ((5*s^2 + 9*s + 9))/(15*s^5 + 47*s^4 + 117*s^3 + 161*s^2 + 81*s)3- Use dimensional analysis to show that in a problem involving shallow water waves, both the Froude number and the Reynolds number are relevant dimensionless parameters. The wave speed c of waves on the surface of a liquid is a function of depth h, gravitational acceleration g. fluid density p, and fluid viscosity μ. Manipulate your's to get the parameters into the following form: Fr= √=f(Re) where Re=pch μ h Too 8 P₂ μ
- (Q-4) Balance the meter stick with two weights and a rock. 0 cm 100 cm Jrock 100g position (cm) weight (gwt) lever arm (cm) torque (gwt cm) Rock 10.60 XXXXXX XXXXXXXX Weight 1 구군, 60 150 cw Weight 2 93.5 100 (Q-5) Assume that the torques balance and use this fact to calculate the weight of the rock. Z Tecw Złcw = WrackFit a power law model to the rheological behavior presented in the data: T [=]D/cm^2 y[=]1/2 1 3 2 - 3 30 4 52 5 80 6 100 7 130 8 160 9 175 10 190 11 218 12 240 13 265 (The second data in the table is not necessary to solve it.)Help yourself with matlab to solve it with the following formula: (Photo)Here I'm finding final kinetic energy KE2, given initial kinetic energy, initial force, alpha N/m^3 and beta N representing F(x). I integrated F(x)dx though I'm not sure how to integrate Fo with respect to X. I tried just finding the integrand ouput of 7.5x10^4m and subtracting the initial force, since the initial force would count as x=0, or I assumed. I then followed the regular approach of adding over the initial KE1 to isolate the unknown KE2 which I keeo getting as 1.07x10^10 which seems to be off. Again, I suspect where I'm going wrong is integrating the initial force -3.5x10^6N with respect to x, but other than what I've already done, that doesn't make sense to me.
- The conduction heat transfer in an extended surface, known as a fin, yields the following equation for the temperature T, if the temperature distribution is assumed to be one-dimensional in x, where x is the distance from the base of the fin, as shown in figure: To Fin >X T(x) h,T Heat Loss d²T_hp (T-T) = 0 dx² ΚΑ dT dx = 0 Here, p is the perimeter of the fin, being 2R for a cylindrical fin of radius R; A is the cross-sectional area, being R2 for a cylindrical fin; k is the At x = 0: T = T₁ dT At x=L: :0 dx thermal conductivity of the material; T is the ambient fluid temperature; and h in the convective heat transfer coefficient. The boundary conditions are as follows: where L is the length of the fin. Solve this equation to obtain 7(x) by using Euler's method for R=1cm, h= 20 W/m².K, k = 15 W/m-K, L = 25 cm, T₁ = 80°C, and T = 20°C.What mathematical relationship exists between the wave speed and the density of the medium, using the POWER trendline equation from the graph? Make your response specific (i.e., describe the full mathematical proportionality between the two variables) Feel free to use the table. Table: Frequency (Hz) Density (kg/m) Tension (N) Speed (cm/s) Wavelength (cm) 0.85 0.1 4.0 632.5 744.12 0.85 0.7 4.0 239.0 281.18 0.85 1.3 4.0 175.4 206.35 0.85 1.9 4.0 145.1 170.70examples, by conering them mer and then trying to draw the paral law, and thiking about how the sine and conine laws re sed to d the mknowns Then before solhing any of the problems, try and sntve some of the Fundamental Problems given on the next page. The solutiuns und answers to these are given in the back of the boik. Doing this throuphout the book will help immensely in developing your problem-solving skills 1%19 |. A 1:-1 lec.2.pdf 2.3 VECTOR ADDITION OF FORCES 27 FUNDAMENTAL PROBLEMS* F2-1. Determine the magnitude of the resultant force acting on the screw eye and its direction measured clockwise from the x axis F2-4. Resolve the 30-lb force into components along the r and raves, and determine the magnitude of each of these components 30 Ib ŽAN 6KN 12-1 F2-4 12-2. Two forces act on the hook. Determine the magnitade F2-5. The foroe = 450 Ih acts on the frame. Resolve this force into eomponents acting along members AB and AC, and determine the magnitude of each component. of the…
- Please solve this problem, Thank you very much! Figure is attached 1. liquids in rotating cylinders rotates as a rigid body and considered at rest. The elevation difference h between the center of the liquid surface and the rim of the liquid surface is a function of angular velocity ?, fluid density ?, gravitational acceleration ?, and radius ?. Use the method of repeating variables to find a dimensionless relationship between the parameters. Show all the steps.**Problem 1.15 Suppose you wanted to describe an unstable particle, that spon- taneously disintegrates with a "lifetime" t. In that case the total probability of finding the particle somewhere should not be constant, but should decrease at (say) an exponential rate: too P(t) = | V(x,1)1²dx = e=1/*. -0- A crude way of achieving this result is as follows. In Equation 1.24 we tacitly assumed that V (the potential energy) is real. That is certainly reasonable, but it leads to the "conservation of probability" enshrined in Equation 1.27. What if we assign to V an imaginary part: V = Vo – ir, where Vo is the true potential energy and r is a positive real constant? (a) Show that (in place of Equation 1.27) we now get dP 21 = --P. dt (b) Solve for P(1), and find the lifetime of the particle in terms of r.Check the following equation for dimensional homogeneity: mu = (Fcos) at where m is mass, v is velocity, F is force, is an angle, and it is time. Check that each term in the equation has the following dimensions: [MOLT] where you are to choose the coefficients a, b, c. Answers: b= C= i i