# Search results

1. ### 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...
2. ### 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...
3. ### 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...
4. ### 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...
5. ### 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...
6. ### 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...
7. ### 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...
8. ### 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...
9. ### 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...
10. ### 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...
11. ### Problem with differentiation and area of components

Homework Statement The diagram attached shows a solid engineering component which consists of a solid cylinder of length L and radius r, together with a right circular cone with semi-vertical angle = 11 degrees. The total surface area of the component is 481. The component is to be...
12. ### Problem with angles and differentiation

Homework Statement A "big screen" AB of height L is placed at a height h above a point C on the ground as shown (in the attachment). A person wishes to sit on the ground at a point D in order to watch a video on the big screen. She wishes to sit at a horizontal distance x away from C which...
13. ### Matrix determinant problem

Homework Statement The matrix A is given as: [25 , 5] [-150 , -30] find, in terms of m, the expression det(A-mI). This will be in a quadratic expression in m. Homework Equations det(A) = ad-bc The Attempt at a Solution i have no idea how to approach this but i...
14. ### Perpendicular unit vector

Homework Statement Given that a = (-1,16,-1) and b = (-18,-15,-15), find the unit vector which is perpendicular to the plane containing a and b. There are two possible answers. Choose the answer with a positive x component. Homework Equations (a*b) = (a2*b3-a3*b2)i -...
15. ### Problem with vectors and unit vectors

Homework Statement An electric charge e which moves through a material of permeability μ with a velocity v, produces a magnetic field β at a point r given by: β= ((μ*e)/(4*∏))*((v*ru)/(|r|)2) where ru is a unit vector in the direction of r. Find β if v=4i+3j+3k and r=4i+7j+5k. Take...
16. ### Trig identity problem

Homework Statement the problem is: tan(theta) = cos(theta) find theta: -pi < theta < pi Homework Equations tan(theta)=sin(theta)/cos(theta) sin^2(theta)+cos^2(theta)=1 The Attempt at a Solution