If you wish to be able to provide answers at anytime, anywhere, or Just-In-Time solutions for your design needs, there are some simple and specially engineered design tool or calculation software that can help you to lessen your unnecessary stress or frustration at work.
Over the years, I have been trying to improve myself constantly on efficiency and productivity aspects of my daily engineering tasks….. still on-going and on-going; lifelong learning! This is trying to move myself towards still-lower and still-competitive cost.
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Work smart! More often than not, we don’t need complex and complicated design tool to solve simple engineering calculations. The fact is that the result outputs remain as an approximation of reality. Easy to use and knowing its limitations are more important than anything else…. speed counts.
Allow me to borrow the theme of the following question, can you solve it within a minute?
Engineers are taught to tackle problems in the real field in a systematic way, starting from the first principle. So let’s solve the above interesting problem in an engineering way that our lecturers or seniors have taught us.
assign variables: h=hat, d=driver, s=spanner.
derive equations:
eqn(1): h+d=1
eqn(2): d+s=2
eqn(3): h+s=2.4
3 unknown variables, 3 equations, so no need iterations!
from eqn(1): -> d=1-h
from eqn(2) -> d=2-s
so, 1-h=2-s
-> s-h=1 …… eqn(4)
from eqn(3), s=2.4-h
substitute s into eqn(4), -> 2.4-h-h=1
-> 2h=1.4
=>h=0.7 (answer 1) ….horray!
now, continue to find d & s
:
:
:
so, how long did I take??
Gaussian Elimination Method
Engineers like to use Gaussian elimination method for solving systems of linear equations. With the help of computing (apps), solving systems of linear equations become easy. For the above example, the 3 equations can be re-written to give the following linear system:
1h + 1d + 0s = 1
0h + 1d + 1s = 2
1h + 0d + 1s = 2.4
The augmented matrix is as follows:
(1 1 0 | 1)
(0 1 1 | 2)
(1 0 1 | 2.4)
And the result is shown below:
(1 0 0 | 0.7)
(0 1 0 | 0.3)
(0 0 1 | 1.7)
[solutions: h=0.7, d=0.3, s=1.7]
The Egg Basket Problem (Example of Applications in Computing)
Given the amount of complexity in the world today, knowing how to tackle the problem in a simple and faster way is the key to sustain a business. Theoretically, the Egg Basket problem is to be solved using the Chinese Remainder Theorem. However, think like an engineer, I will solve it in an engineering way – simple and efficient! The engineering solution is actually very simple: the iterative approach. As shown in the image below, I have built a Windows program to solve the Egg Basket problem. You can download the Egg Basket solver program (free with no ads, no setup requirement) and try it.
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