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    Modes of Vibration of 3-DOF Spring Mass System

    1. Homework Statement 2. Homework Equations a11 = a21 = a31 = a12 = a13 a22 = a32 = a23 $$ \begin{bmatrix} x_{1} \\ x_{2} \\ x_{3} \end{bmatrix} =ω^2m \begin{bmatrix} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} &...
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    Heat Loss Through a Short Cylinder

    1. Homework Statement A short metal cylinder 145 mm in diameter and 145 mm high at 1045 K is suddenly exposed (all sides exposed) to a room air temperature at 300 K with h=25 W/m².K. Assume that for the metal k=40W/m.K, den=7800 kg/m3 and Cp=c=600 J/kg.K. Estimate (a) the time required for...
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    Thermodynamics Gas Mixture - Dew Point Temperature

    1. Homework Statement Only Number 1, not number 2 2. Homework Equations Dew Point Temperature T = Saturated Temperated at Vapor Pressure Partial Pressure = (mole fraction) x (Mixture Pressure) 3. The Attempt at a Solution The dew point temperature is only dependent on the pressure of...
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    Gas Mixture - Dew Point Temperature

    1. Homework Statement Only Number 1, not number 2 2. Homework Equations Dew Point Temperature T = Saturated Temperated at Vapor Pressure Partial Pressure = (mole fraction) x (Mixture Pressure) 3. The Attempt at a Solution The dew point temperature is only dependent on the pressure of...
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    DC Shunt Motor

    1. Homework Statement A 250V shunt dc motor runs at 1000rpm while taking a current of 25 A. The motor has armature and field resistance as 0.2W and 250W respectively. Calculate (a) The speed when the load current is 50A. (b) Armature torque developed at both speeds. 2. Homework...
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    Power Correction Unity

    1. Homework Statement Not sure if this is the correct place for Electrical Engineering Homework help but here goes A single-phased motor connected across a 240-V source at 50Hz as shown in the figure has a power factor of 1.0, I = 20A, I1 = 25 A. Find the capacitance required to give a unity...
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    Frequency of gears (given frequency of shaft)

    1. Homework Statement 2. Homework Equations tangential velocity v = ωr angular velocity ω = 2πf 3. The Attempt at a Solution Not really looking for help to solve the problem. I'm just confused about the speed/angular velocity and frequency If the frequency of the motor is given as 24...
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    Theorems of Pappus (Finding mass)

    1. Homework Statement A steel die, shown in section, has the form of a solid generated by revolving the shaded area around the z-axis. Calculate the mass m of the die. 2. Homework Equations V =θ(rA) where r is the distance from the origin to the centroid of each shape m = ρV where ρ =...
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    Falling Through Earth's Center

    1. Homework Statement With what speed would mail pass through the center of earth if falling in a tunnel through the center? 2. Homework Equations W = -K K = 0.5mv^2 (vf)^2 = (vi)^2 + 2aΔx 3. The Attempt at a Solution My main question is why can't I use the last equation...
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    Rotational Inertia about Rotation Axis Through COM

    1. Homework Statement A constant horizontal force of magnitude 10 N is applied to a wheel of mass 10 kg and radius 0.30 m as shown in the figure. The wheel rolls smoothly on the horizontal surface, and the acceleration of its center of mass has magnitude 0.60 m/s2. (a) What are the...
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    Linear Speed of Earth at latitude 40° N

    1. Homework Statement a) What is the angular speed ω about the polar axis of a point on Earth's surface at latitude 40° N? (Earth rotates about that axis.) I solved this part b) What is the linear speed v of the point? 2. Homework Equations v = ωr where r = radius of Earth at latitude 40°N...
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    Friction Force and Motion

    1. Homework Statement You testify as an "expert witness" in a case involving an accident in which car A slid into the rear of car B, which was stopped at a red light along a road headed down a hill. You find that the slope of the hill is θ = 12.0°, that the cars were separated by distance d =...
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    Center of Mass (Triple Integral)

    1. Homework Statement T is the solid bounded by the cylinder y^2+z^2=4 and the planes x=0 and x=3. The mass density at a point P of T is directly proportional to the distance between P and the yz-plane. Find the center of mass of the solid T. 2. Homework Equations y^2+z^2=4 x=0 x=3 3...
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    Finding absolute extrema with only 1 critical point

    1. Homework Statement Edit: Not absolute, just extrema I've already found the critical point to be (-1/2, -1/4, 1/2) with a value of -1/2. My only problem is finding whether this is a max or min. What technique do I use to find out? I don't believe I can use the 2nd derivative test because all...
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    Absolute Extrema: 2 variables

    1. Homework Statement Find the absolute extrema of the function on the set D. f(x,y)= x^2 + 4y^2 + 3x -1 D= {(x,y) l x^2 + y^2 ≤ 4} 2. Homework Equations 3. The Attempt at a Solution The only thing I've done so far was find the critical point. I found f-sub x = 2x+3 and...
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    Torque about P (Cross Product?)

    1. Homework Statement 2. Homework Equations The book says that Torque = the length of the moment arm X the magnitude of the vertical component of F = r X F 3. The Attempt at a Solution My problem is that I don't have any vectors to do a cross product. Instead...
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    Angle between intersecting vectors

    1. Homework Statement Given 2 lines, determine whether they are intersecting or not. If they are, determine the angle between them. Line(1): x = 1-t, y = 3-2t, z = t Line(2): x = 2+3t, y = 3+2t, z = 1+t 2. Homework Equations cos(theta) = (a·b)/(\left|a\right|\left|b\right|) 3...
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    Taylor Polynomial of Smallest Degree to approximation

    Hey, guys. Having problems with this question because I don't exactly know how to begin it. 1. Homework Statement The problem states to: "Find the Taylor polynomial of smallest degree of an appropriate function about a suitable point to approximate the given number to within the indicated...
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    Indeterminate Forms and l'Hopital's Rule

    1. Homework Statement Lim as x→∞ of ((2x+1)/(2x-1))^(sqrtx) 2. Homework Equations 3. The Attempt at a Solution When I initially plugged in ∞ for my x, I get (∞/∞)^∞, correct? If so, should I just let y=((2x+1)/(2x-1))^(sqrtx) and take the limit of both sides using ln? That's what I...
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