I'm not sure if this is the appropriate place, but I've just been searching, with no luck, on how to solve a spring system with RK4 (hence the math section, since it's a Runge Kutta question). How would you set it up to change position based on spring properties? I haven't really found any...
1. Homework Statement
Program, without any built in functions (like ODE45), a solution to the Blasius Equation in Matlab that outputs boundary layer profiles for given x values, u values, etc.
2. Homework Equations
2f''' + f''f = 0
fj = fj-1 + Δη/2 * (gj + gj-1)
gj = [Δη2/4][2gj+1/Δη2 +...
1. Homework Statement
Find the transfer function for the following mechanical system with force input fin and output x2.
2. Homework Equations
3. The Attempt at a Solution
The reason I left the equations blank is because I'm not sure how to appropriately model this scenario. I've seen two...
1. Homework Statement
Find a differential equation that describes the circuit that includes only vin and vout as variables.
2. Homework Equations
C(dvin - dvout)/dt = i
vin - vout = L(di/dt)
3. The Attempt at a Solution
So the answer I got was:
C(d2vout/dt2) + vout = LC(d2vin/dt2)
My...
1. Homework Statement
As water flows through the pipe at a velocity of 5 m/s, it encounters the orifice plate, which has a hole in its center. The pressure at A is 255 kPa , and at B it is 180 kPa, Assume water is ideal fluid, that is, incompressible and frictionless. Determine the force the...
1. Homework Statement
The apparatus or "jet pump" used in an industrial plant is constructed by placing the tube within the pipe. The velocity of the flow within the 200-mm-diameter pipe is 2 m/s, and the velocity of the flow through the 20-mm-diameter tube is V = 37 m/s . The fluid is ethyl...
1. Homework Statement
Water exits the 3-in.-diameter pipe at a velocity of 12 ft/s and is split by the wedge diffuser. Assume water is ideal fluid, that is, incompressible and frictionless. Determine the force the flow exerts on the diffuser. Take θ = 30 ∘
2. Homework Equations
F = ρAV
3...
I'm trying to find gauge pressure at multiple points in a "mixed" container. Which, I thought would be equal to ρghliquid 1 + ρghliquid 2 etc. Well, that's not right? And I don't know why?
So for point A, I did: (55.1 * 32.1 * 4) + (62.4 *32.1 * 4). Then I divided by 144 to get it into psi. I...
1. Homework Statement
A fluid has velocity components of u=[30/(2x+1)]m/s and v=(2ty)m/s,where x and y are in meters and t is in seconds. Determine the equation of the streamline that passes through point (2 m, 6 m) at time t = 2 s. Write the equation in the form y={y(x)}m, where x is in...
I'm working on a problem and need to find quality, mass, and pressure. I'm given a temperature (2°C), a volume (1200m^3), and a percent volume occupation (1% saturated liquid). Is it "legal" to use the saturated liquid tables, at 2°C, to find the volume or pressure (I forget which one we were...
1. Homework Statement
The conical bearing is placed in a lubricating Newtonian fluid having a viscosity μ.
Determine the torque T required to rotate the bearing with a constant angular velocity of ω. Assume the velocity profile along the thickness t of the fluid is linear.
2. Homework...
So I'm studying for an upcoming Mechanics of Materials exam. Gotta ace it! Anyways, I'm having trouble with these types of problems. Finding state of stress on a point in 3D. This picture comes from: http://www.academia.edu/6204133/Chapter_09
Which has worn shown, but not explanations. I have...
1. Homework Statement
Find the average power dissipated in the 30 Ω resistor in the circuit seen in the figure if ig=7cos20,000tA.
2. Homework Equations
KVL/KCL equations
P=VI* (possibly) or I^2(R)
3. The Attempt at a Solution
I tried to do a mesh, but got I∆(60-j130) = 0, which isn't right...
1. Homework Statement
(in picture)
2. Homework Equations
V=IZ
3. The Attempt at a Solution
So last time I had to do KCL to find voltages, so I want to make sure I'm doing this one right. Can I do voltage division and do Vload/VG?
My division would be VG(500<36.87)/(500<36.87 + 60<53.13)...
1. Homework Statement
(in picture)
2. Homework Equations
V=IZ
All the ratio formulas (i.e. V2/V1 = N2/N1)
3. The Attempt at a Solution
I thought V1 would be 1000 Vrms. Well the answers are shown and it's not. So I thought maybe I would multiply Vrms (1000) by root 2 to find Vpeak (Vrms =...
1. Homework Statement
For the circuit in (Figure 1) , suppose
va=10cos16,000tV
vb=20cos4000tV.
Suppose that R = 700Ω .
Write the steady-state expression for io(t) as io=I′ocos(ω′t+ϕ′)+I′′ocos(ω′′t+ϕ′′), where −180∘<ϕ′≤180∘, −180∘<ϕ′′≤180∘, and ω′>ω′′. Find the numerical value of I′o.
Find...
1. Homework Statement
Determine the state of stress at point A on the cross section of the beam at section a−a. TakeP = 33kN .
2. Homework Equations
σ = My/I
3. The Attempt at a Solution
Moment = Fd = 33000N(500mm) = 165000000
Y = 90.71 (100-9.29, 9.29 being the Ybar of the little piece)
I...
1. Homework Statement
Determine the state of stress at point A on the cross section at section a−a of the cantilever beam. Take P = 350kN .
2. Homework Equations
Um . . . σ = P/A ?
3. The Attempt at a Solution
Yeah I'm not quite sure. I thought it was P/A, using 350000N as "P" and...
1. Homework Statement
Find V0 using voltage/current division
2. Homework Equations
V=(VsR)/Req
I=(IsIeq)/I
3. The Attempt at a Solution
I used general circuit rules (parallel and series) to get the total resistance as 14.775 ohms{?}. And I'm stuck with what to do next . . .
1. Homework Statement
The following shows a cross section through a tank with a rectangular sloping gate that is 10 m long and 4 m wide (width is measured into the page). The gate is hinged along its top edge and held closed by a force at its bottom edge at A that acts perpendicular to Gate AB...
1. Homework Statement
Determine the product of inertia of this area with respect to the centroidal x′ and y′ axes.
Locate the centroid x bar of the beam's cross-sectional area. Set a = 120mm , b = 290mm , d = 30mm , h = 390mm .
2. Homework Equations
???
3. The Attempt at a Solution
So I...
1. Homework Statement
The switch has been open for a very long time, and then we close it. In the instant right after we close the switch, assuming that...
1. Homework Statement
A 1.60 m long rod rotates about an axis through one end and perpendicular to the rod, with a rotational frequency of 6.91 radians per second. The plane of rotation of the rod is perpendicular to a uniform magnetic field of 0.30 T. Calculate the magnitude of the mf induced...
1. Homework Statement
If a current I=4 A exists between points a and b, R1=6 http://loncapa.mines.edu/adm/jsMath/fonts/cmr10/alpha/100/char0A.png, [Broken] R2=6 [PLAIN][PLAIN]http://loncapa.mines.edu/adm/jsMath/fonts/cmr10/alpha/100/char0A.png, [Broken] V1=16 V, and V2=6 V,the voltage...
1. Homework Statement
The schematic shows a low-pass filter identical to the one you built in studio. This filter uses a 60 k resistor and a 250 pF capacitor, and the input signal is at 30 kHz. (1 pF=10−12 F)...
1. Homework Statement
Nerve signals in the body occur when a small voltage, called an action potential, is applied across the membrane of a cell. When this action potential is applied across a region of the cell membrane called an ion channel, current in the form of moving potassium ions will...
1. Homework Statement
A wire with cross-sectional radius 0.91 mm lying along the x axis from x=0 to x=0http://loncapa.mines.edu/adm/jsMath/fonts/cmmi10/alpha/100/char3A.png90 [Broken] m is made of an alloy that varies with its length in such a way that the resistivity is given by...
1. Homework Statement
Convert to the two other coordinate systems: θ = π/4
2. Homework Equations
tan = x/y
r = √(x^{}2 + (y^{}2)
3. The Attempt at a Solution
The tangent equals one, so doesn't this make just the line x = y? But the cylinder (I'm assuming since the second part is the same...
1. Homework Statement
Determine the magnitude of the projection of force F = 700N along the u axis.
2. Homework Equations
Cosθ = (A • B)/(||A|| * ||B||)
3. The Attempt at a Solution
I'm guessing I have to use the above equation, but my problem is finding the B vector. A is easy...
1. Homework Statement
Determine coordinate direction angle γ of the resultant force acting at B.
2. Homework Equations
Cos\gamma = F\underline{}z/F
3. The Attempt at a Solution
The first part was to find magnitude of F\underline{}b. The next part was finding the other...