 
Summary: MATH 336 Extra Review Questions for Exam 3
1. A mass of 2 kg is attached to a spring and moves on a frictionless horizontal surface. A force
of 18 Newtons stretches the spring 1 m. At time t = 0, the body is 1 m to the right of its
equilibrium position, and is moving to the left at 3 m/sec.
(a) Set up the differential equation and initial conditions for the position x(t) of the body
at time t.
(b) The solution of the initial value problem can be written in the form x(t) = C cos(0t).
Determine 0, C, and .
2. Use the definition of the Laplace transform to determine F(s) = L{te2t
}. Also indicate the
values of s for which F(s) is defined.
3. Determine the inverse Laplace transform of the following functions.
(a) F(s) =
2s + 1
(s2 + 4)
(b) F(s) =
2s + 1
s(s2 + 4)
4. Use Laplace transforms to solve the initial value problem
x + 9x = et
