Further Maths and Simulation
1: The admittance, ?, in a circuit is given by
? =
1
?
where ? is the impedance of the circuit. If Z = 150 − j22, find ?.
5 marks
2: By applying Kirchoff’s laws on a circuit, the following mesh equations were obtained:
18?1 + ?12?1 − ?25?2 = 200
20?2 + ?40?2 + 15?2 − ?25?1 = 0
Determine, in polar form, the primary and secondary currents, ?1and ?2 respectively,
through the circuit.
12 marks
3: If 6?
2 + 3?
2 + ? = 1, find the rate at which ? is changing with respect to ? at the
point (3, 5, 2)
4 marks
Course: B.Eng/M.Eng Engineering Year 2
Module: Further Maths and Simulation (SC2153)
Topic: Assignment 1
4: The stream function, ? (?, ?),has a circular
function shape as shown, and is related to the
velocity components ? and ? of the fluid flow by
? =
??
?? and ? =
??
??
a) If ? = ??√?
2 + ?
2, find ? and ?.
b) The flow is irrotational if ? satisfies Laplace’s equation,
?
2 ?
??2 +
?
2?
??2 = 0
Determine if the flow is irrotational.
15 marks
5: Determine the force, F, which has a magnitude of 64kN in the direction of the vector
?? where A = (2, 4, 6) and B = (6, 3, 4).
8 marks
6: An object is dropped and its position vector, r, is given by
? = (?
5 − 2?
2
)? + (7?
3 − 6?
2
)?
a) Find the velocity, ?, and the acceleration, ?.
b) What is the angle between ? and ? when ? = 2?
12 marks
Course: B.Eng/M.Eng Engineering Year 2
Module: Further Maths and Simulation (SC2153)
Topic: Assignment 1
7: If ? = ??
2 + 3??
2 + ??
2
a) Determine grad ? at the point (3, 5, 1).
b) Find the direction from the point (1, 1, 0) which gives the greatest rate of
increase of the function of ?.
9 ma