Question

DIFFÉRENTIEL EQUATIONS

We consider 2 coupled harmonic oscillators, as shown in the diagram below.

m! m2 F(t) win 01 x1(1) 02 x200) X

The mass m1 is subjected to an external force F (t).

1. Construct the system of differential equations whose unknowns are the displacements x1 (t) and x2 (t) of each of the 2 masses (DIFFERENTIEL EQUATIONS).

2. Solve x1 (t) and x2 (t) in the case where m1 = 1kg; m2 = 2kg; k = 1 N / m; F (t) = 0 and x1 (0) = 0; ?1 ′ (0) = 0; x2 (0) = 0; ?2 ′ (0) = 0

3. Solve x1 (t) and x2 (t) in the case where m1 = 1kg; m2 = 2kg; k = 1 N / m; F (t) = cos (t) and x1 (0) = 0; ?1 ′ (0) = 0; x2 (0) = 0; ?2 ′ (0) = 0

Answer 1

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