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    Misc. Hydrostatics problem in a water vessel

    I am trying to design a water vessel system that maintains it's water level as it is consumed. In item 1. It's a simple water barometer, where the height of water in the column can be supported by atmospheric pressure until 10.34. In item 2. There are two columns that are open to atmosphere...
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    Calculating Power at source from Intensity at distance R

    Homework Statement An enclosed chamber with sound absorbing walls has a 2.0 m × 1.0 m opening for an outside window. A loudspeaker is located outdoors, 46 m away and facing the window. The intensity level of the sound entering the window space from the loudspeaker is 42 dB. Assume the acoustic...
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    Richardson Extrapolation with 3 steps?

    Homework Statement [/B] use richardson extrapolation to estimate the first derivative y=ln(x), x=5 using steps of 2, 1, 0.5. Four decimal points. obtain true relative error for the last estimate and comment on its value. Homework Equations [/B] deriv ln(x)=1/x The Attempt at a Solution I...
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    Differential Equations System Solutions

    Homework Statement Consider the initial value problem for the system of first-order differential equations y_1' = -2y_2+1, y_1(0)=2 y_2' = -8y_1+2, y_2(0)=-1 If the matrix [ 0 -2 -8 0 ] has eigenvalues and eigenvectors L_1= -4 V_1= [ 1...
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    High order differential equations: undetermined coefficients

    Homework Statement If the method of undetermined coefficients is used to find a particular solution yp (t) to the differential equation y'''-y'=te^(-t)+2cos(t) should have the form: ? Homework Equations The Attempt at a Solution LHS r^3-r=0 roots= 0, 1 y_c(t)=c_1e^t RHS...
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    2nd order differential equation: undetermined coefficients

    Homework Statement y''-y=t-4e^(-t) Homework Equations method of undetermined coefficients The Attempt at a Solution solving for characteristic equation first y''-y=0 r^2-1=0 c_1e^(-t)+c_2e^(t) RHS particular solution t-4e^(-t) y_p(t)= At+B+Ce^(-t) y_pt'(t)=A-Ce^(-t)...
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    Conservation of Energy falling rod

    Homework Statement A uniform ladder having mass 14kg and length 3m is released from rest when it is in the vertical position. If it is allowed to fall freely, determine the angle Theta at which the bottom end A starts to lift off the ground. For calculation assume the ladder is a slender rod...
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    Wind Turbine Question

    Homework Statement During a sustained wind the blades on a two blade horizontal–axis wind turbine is turning with an angular velocity of 5 rad/s. If initially the blades have an angular velocity of 2 rad/s, determine the distance point P on the tip of the blade has travelled in 3.0 seconds...
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    Differential equations - backwards problem

    Homework Statement If y=y(t) is the solution of the initial value problem { y'+(2t+1)y=2cos(t) y(0)=2 then y''(0)=? it is a multiple choice practice problem with choices y''(0)=2 y''(0)=-2 y''(0)=4 y''(0)=0 y''(0)=-4 Homework Equations The Attempt at a Solution Im really not sure how...
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    Differential Equations: Bernoulli Equation

    Homework Statement Find the general solution: y'-3y=(y^2) Homework Equations The Attempt at a Solution divide both sides by y^2 y'(y^-2) -3(y^-1) = 1 we know v=y^(n-1) v=y^-1 v'=d/dx(y^-1) v'=-(y^-2) y' plug it back into y'(y^-2) -3(y^-1) = 1 -v'-3v=1 this is where I think I am...
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    Kinematics Question. Incline, Spring, Friction

    Homework Statement Practice problem for midterm. Homework Equations [/B] T_1+U_1=T_2+U_2 U_spring=1/2kx^2 The Attempt at a Solution [/B] Set X-axis along the 30 degree line and the Y-axis perpendicular. I'm not sure how to consider the friction constant into the formula. Any help is...
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    Finding the zeroes for cubic equation

    Homework Statement Find all zeroes for the function f(x) f(x)=x^3+25x Homework Equations The Attempt at a Solution I tried factoring out x out of it. x(x^2+25) and again to give x[(x+5i)(x-5i)] this would give me the 0,-5i,+5i as the zeroes. Doesn't seem to be right though. Any...
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    Rotation matrix vs regular matrix

    Can you calculate eigenvalues and eigenvectors for rotation matrices the same way you would for a regular matrix? If not, what has to be done differently?
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    Linear algebra matrices multiplication (transpose)

    Homework Statement We are looking for the matrix A Homework Equations (A^transpose)^transpose=A The Attempt at a Solution i would start with finding the transpose of the matrix. -5 0 -8 -7
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    Single Photon/Indistinguishabiliity principle experiment

    If a single photon light source shoots a photon through the "attached" path. What is the percentage of the photon will make it to each detector. The light source is the box, the photon trajetory is yellow, beamsplitter is blue, mirror is black, detectors are purple, and obstacle is red. I think...