AREAS OF CONCENTRATION EMT 201 FINAL EXAM
ENGINEERING MATHEMATICS 1 FIRST SEMESTER 2013/2014
ENGINEERING MATHEMATICS 1 FIRST SEMESTER 2013/2014
Due to the wide coverage of our course EMT 201 I advise to concentrate
on the following exercises. Similar exercises will be coming out in the final
exam.
1. A tank contains 234 liters of
water. A bitter lemon solution containing 5 kg/liter of sugar enters the tank
at the rate of 6 liters/min and runs out at 4 liters/min. The tank has a paddle
that keeps stirring to keep the mixture uniform. Find the amount of sugar in
the tank after 30 minutes. Solve by ODE method.
2. A student deposited N100000.00
at an annual rate of 8% compounded continuously, how long will it take the
amount to double in value? Solve by a) ODE b)
Laplace
3. Solve the
first order linear DE a) y’ – 6y =12. b) y’ + 5xy = 10x.
4. How much will be left after
500 years for a radioactive elements carbon 14 which has a half life of 5750
years if the initial amount is 50 grams? Solve by ODE and Laplace transform
methods.
5. Solve the equation y” +y’ –6y
= e 4x by a)
undetermined coefficient method b) variation of parameters
7. Solve the initial value DE y’ – 3y=0, y (0) =1,
find the value of y (0.4) using a) ODE
b) Laplace c)
Power series D) Euler’s numerical
method with N=4.
8. Find the equation of motion of
a 4 kg mass suspended to a coiled spring
with k = 100 N/m, initially displaced a distance of 1 meter from equilibrium
position, and released with zero velocity and subjected to no damping or
external forces. Find a) Equation
of motion by ODE and Laplace methods b)
amplitude c) angular frequency d) natural frequency e) Period f) graph of the curve
![]() |
Mathematics Text?Workbook |
No comments:
Post a Comment