BMath Bachelor of Mathematics Bachelor of Mathematics: Applied Mathematics Problem Solving 2

Question 1

A mass-spring system obeys m·x'' + kx = 0. If m = 4 kg and k = 16 N/m, what is the angular frequency ω?

Accepted Answer

2 rad/s

Answer

ω = √(k/m) = √(16/4) = √4 = 2 rad/s.

Question 2

Using Euler's method with step size h = 0.1 to solve y' = y, y(0) = 1, what is the approximation for y(0.1)?

Accepted Answer

1.1

Answer

Euler's step: y₁ = y₀ + h·f(x₀,y₀) = 1 + 0.1·1 = 1.1.

Question 3

What is the Fourier series representation of an odd function on [-π, π]?

Accepted Answer

It contains only sine terms

Answer

An odd function satisfies f(-x) = -f(x), so all cosine (even) coefficients vanish, leaving only sine terms.

Question 4

The Laplace transform of e^(at) is:

Accepted Answer

1/(s - a)

Answer

L{e^(at)} = ∫₀^∞ e^(at)e^(-st)dt = 1/(s-a) for s > a.

Question 5

In linear programming, the optimal solution of a bounded feasible region always occurs at:

Accepted Answer

A vertex (corner point) of the feasible region

Answer

The fundamental theorem of linear programming states the optimum is attained at a vertex of the convex feasible region.

BMath Bachelor of Mathematics Practice Test