Assignment for CODs
Due date: 29-01-2022
Max.Marks: 10
Question 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Use the Laplace transform technique to solve the initial value problems
y 0 + 4y = g(t), y(0) = 2
where


0 0 ≤ t < 1
g(t) = 12 1 ≤ t < 3


0 t≥3
Question 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A 16 lb weight is attached to a spring with a spring constant equal to 2 lb/ft. Neglect damping. The
weight is released from rest at 3 ft below the equilibrium position. At t = 2π sec, it is struck with a
hammer, providing an impulse of 4 lb sec. This situation is modeled by the initial value problem
16 00
y (t) + 2y 0 + 10y = 4δ(t − 2π), y(0) = 3, y 0 (0) = 0
32
Determine the displacement function y(t) of the weight.
Question 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Let f (x) = e−b|x| for all real x, with b, a positive constant. Compute the Fourier transform.