Final exam emt 201 review. Study the following problems. Similar exercises will be given on final exam.

1. A 4 kg mass suspended to a coiled spring with k = 484 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. Determine a) the equation of motion using Ordinary DE and Laplace transform solutions b) amplitude c) natural frequency d) period of motion e) graph the equation.

2. How much will be left after 500 years for a radioactive element which has a half life of 2000 years if the initial amount is 40 grams? Solve by a) Ordinary DE solution b) Laplace transform.

3. Solve the non-homogeneous differential equation y” + 2y’ – 8y = e 3x by undetermined coefficient method.

4. A tank contains 200 liters of water. A sweetener containing 2 kg/liter of sugar enters the tank at the rate of 4 liters/min and runs out at 3 liters/min. The tank has a paddle that keeps on stirring in order to keep the mixture uniform. Find the amount of sugar in the tank after 25 minutes.

5. A university canteen serves a cup of tea at 83℃ to an Engineering student. After 2 minutes, the tea has cooled to 73℃. If the canteen temperature is 23℃, how many minutes that the student must wait to cool the tea to 54℃ ?

6. A football superstar was found dead at 6 pm in a room temperature of 22 C. His dead body temperature was 28C upon discovery. If a person’s temperature was 37C and cools down to 35 C after 2 hours after death, determine what time the murder was committed? Use Newton’s law of cooling. Solve by an ordinary differential equation method.

7. Solve DE y’ – y = 0, y(0) = 1. Find y (0.8) using a) ordinary DE method b) Laplace transform c) Power series d) Euler’s method with n= 4.

8. A Petro chemical company uses 900 m3 wastewater tank to control the flow of toxic wastes to its treatment pond. The tank initially has a 160m3 of wastewater containing 1 kg toxic wastes per m3 wastewater. A wastewater containing 1.5 kg toxic wastes per m3 enters the tank at 40 m3/hr and simultaneously released to the treatment pond at 20 m3/hr. A tank has paddle to keep the mixture uniform. Determine the rate, kg toxic/m3 wastewater at which it is released after 5 hours. Solve by ordinary DE method.

9. A tank contains 200 liters of water. A sweetener containing 2 kg/liter of sugar enters the tank at the rate of 4 liters/min and runs out at 3 liters/min. The tank has a paddle that keeps on stirring in order to keep the mixture uniform. Find the amount of sugar in the tank after 25 minutes. Solve by Ordinary DE.

10. A student deposited N300, 000.00 at an annual rate of 8.25 % compounded continuously, how long will it take the account to double in value? Solve by ordinary DE.