Instructions:

1. Use the assignment cover given as your cover report.

2. Submit on (or before) 16 December 2016 before 5.00 pm.

3. Marks will be deducted for copying and late submission will NOT be marked.

4. Each group must present their original work.

5. Plan the task, discuss and understand the problem given, come out with a solution and prepare your report well.

QUESTION 1

Determine the time required to cool down a solid object initially at 80° C to 8°C. It is placed in a refrigerator with its interior air maintained at 5°C. If the coefficient 0.002m^-2s^-1 and the contact area between the solid and the cool air in the refrigerator is A= 0.2m².

What would you do if the required time to cool down the solid is too long?

QUESTION 2 Electric circuits

Figure 1 shows a circuit contains an electromotive force E (supplied by a battery or generator), a resistor R, an inductor L, and a capacitor C, in series. If the charge on the capacitor at time t is Q = Q(t), then the current is the rate of change of Q with respect to t: I = dQ/dt. Applying Kirchhoff's law on Figure 1, the related differential equation is given by :

Ld²Q/dt² + RdQ/dt + 1/C.Q = E(t)

If R= 400, L = 1H, C =16x 10^-4 F, =100 cos10t , and the initial charge and current are both 0,

a) Find the charge in term of t.

b) Find the current in term of t.

c) Sketch graph of current and charge when t= 0,1, 5, 25,125 seconds.

Translate the meaning of the graphs within a short paragraph.

QUESTION 3

Use Laplace Transform to compute the solution to the initial value problem,

x"( t)- 2x'( t)- 3x( t) = e^2t

with x(3) = 1 and x'(3) = 0.

Ordinary differential equation assignment