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2. ### Maximum pull-off load, axial load and radial load of two strapped pipes

Imagine the following scenario. A pipe is strapped to a larger "host" pipe using a steel strap and a spacer block as shown in the image below. If anyone could have a look at my calculations to confirm they are correct that would be brilliant! Variables Assuming the following general values I...
3. ### Vibration of a cantilever beam

Hi there! Im trying to do an analysis in Abaqus of a cantilever pipe, with a tip mass at the free end, that is decelerating to a stop at 10 m/s2 from 10m/s, causing it to vibrate. The pipe is vertical, fixed at the top with the mass at the bottom, and it is moving in the x axis. To validate my...
4. ### Vibration of a cantilever beam

Oh, and I forgot to say that the pipe is vertical and that the velocity and deceleration is in the x axis
5. ### Vibration of a cantilever beam

Hi there! Im trying to do an analysis in Abaqus of a cantilever pipe, with a tip mass at the free end, that is decelerating to a stop at 10 m/s2 from 10m/s, causing it to vibrate. To validate my results im doing some handcalcs. I have done a static analysis and calculated the maximum deflection...
6. ### Optical misalignment

Hi all I was just wondering if anyone could help me with estimating error caused by misalignment of an optical arrangement. I am interested in how the focal length of this arrangement will be affected by say a misalignment of just one of the lenses. I'll assume that every component is aligned...
7. ### Mass Spring Damper Transfer Function

Homework Statement The translational system in the first attachment represents the rear/front suspension of a car of mass 1262kg. The distance between the axles is 2.41m and the distance between the centre of mass and the front axle is 1.22m. I am told that: m2 = 40 kg c1 = 800 Nm/s k1...
8. ### Fourier Series Problem

yeah im getting the right answer now :-) thanks for your help!
9. ### Fourier Series Problem

ahh! ive been using sin instead of cos! i cant believe i did that. so ive integrated 2/T ∫ f(t)*sin(n*π*t/T) dt between 0.5 and 0 and i get: (22*cos(pi*n) - 11*n^2 *pi^2 + 22*n*pi*sin(n*pi) -22)/(2*(n^3 * pi^3)) since ive integrated for only half the period and between 0 < t < 0.5 i...
10. ### Fourier Series Problem

how would you integrate for this problem?
11. ### Fourier Series Problem

so for 0 < t < 0.5, f(t) = 5.5 - 22*t^2 ? then do i add the integral of: f(t)*cos((2*pi*n*t)/T) dt between -0.5 < t < 0 and -f(t)*cos((2*pi*n*t)/T) dt between 0 < t < 0.5 because wont that just equal zero?
12. ### Fourier Series Problem

well im not really sure what to use as the bounds for the integral... i got confused when it said the period was 1 but the function is only true between -0.5 < t < 0. i know since its odd its asymettric about the vertical axis and since its periodic it might have something to do with that? i...
13. ### Fourier Series Problem

Homework Statement f(t) is an odd, periodic function with period 1 and: f(t) = -5.5 + 22*t2 for -0.5 ≤ t < 0 i) find the Fourier coefficient bn ii) find the Fourier coefficient b5 Homework Equations bn = (2/T) * ∫ f(t) *sin((2*n*∏*t)/T) dt between T/2 and -T/2...
14. ### Second order inhomogeneous simultaneous differential equations

yes it is, i was trying that before but my answers kept coming up different to those given. i must have made some mistake when i rearranged the denominator. thanks for your tips :-)
15. ### Second order inhomogeneous simultaneous differential equations

ok i have got the answer for part vi now, thanks lanedance :-) for parts iii and iv, would it be when the denominator is equal to zero?
16. ### Second order inhomogeneous simultaneous differential equations

Homework Statement Vibration in a system can be a source of problems. For example, the deck on a ship could vibrate due to the engine which represents a forcing function. This system may be simply modelled by a mass, representing the deck, a spring representing the stiffness of the deck and a...
17. ### Problem with differentiation to find maximum points

yeah i get that the darkest points as being in the centre of the long sides. so if i differentiate the original equation with respect to h and then set x=0, y=32, x0=80, y0=32 and q=1730600 and solve the equation equal to zero then i will get a value for h that maximises the luminance at these...
18. ### Problem with differentiation to find maximum points

Hi Ray :-) what is Maple? i have Mathcad v15 but i dont really understand how to use the 3d plots feature. is Maple any better? So if i get expressions for the luminance at the both points, the centre of the side and at the corners, what do you then mean by 'find the h-interval'? and how would...

anyone?? :-(
20. ### Problem with differentiation to find maximum points

Homework Statement A sports stadium is lit by four floodlights standing at the four corners of a rectangle which contains the rectangular pitch placed symmetrically inside it. The length of the rectangle is 160 metres and the width is 64 metres. This question is concerned with finding the...
21. ### Differential equation

oh ok, i havent done differential equations in about a year and thats just the method i thought my teacher taught me haha. thanks for setting me straight though guys :-)
22. ### Differential equation

that sounds better than what ive been getting :P how did you get that?
23. ### Differential equation

Homework Statement dT/dt + 0.4*T - 6.4 = 0 where T is the temperature at time t initially the temperature is 86 degrees find the temperature at t=2.3 Homework Equations The Attempt at a Solution so i rearrange the equation to get: dT/dt + 0.4*T = 6.4 then integral...
24. ### Problem with finding multiple solutions to a trigonometric equation

Homework Statement Find all solutions to the following equation: sin((5*x/2)+15)=0.433 where 0 < x < 360 Homework Equations The Attempt at a Solution i can find the first value of x that satisfies this equation. (5*x/2)+15=sin^-1(0.433) 5*x/2=10.6581 5*x=21.2162 x=4.2632...
25. ### Addition of 3d force vectors to find resultant

ahh ok, ive got it now :-) thanks a lot
26. ### Addition of 3d force vectors to find resultant

arent unit vectors = (a.b)/(|a.b|)? would i convert them all into their unit vectors and then multiply by the force acting along them?
27. ### Addition of 3d force vectors to find resultant

well you can say that: 5=((-4*x)^2+(-3*x)^2+(-1*x)^2)^0.5 where x is a constant. once you find x you can multiply the original vector by it to get a vector with magnitude 5 in that direction
28. ### Addition of 3d force vectors to find resultant

im not really sure what you mean? are you saying that if i take the 5N vector acting along (-4,-3,-1) then i can say that that is equal to (-20,-15,-5)?
29. ### Addition of 3d force vectors to find resultant

Homework Statement A force of 5N acts along the vector (-4,-3,-1) A force of 2N acts along the vector (-3,-6,5) A force of 4N acts along the vector (-9,-1,8) find the resultant force vector. Homework Equations The Attempt at a Solution i tried to multiply the vectors by the...
30. ### Problem with differentiation and area of components

yes i have now completed this problem :-) thanks a lot for your hints ;-)