Consider a system of two masses, m1 and m2, connected by three springs with spring constants k1, k2, and k3. The first mass is attached to a fixed wall with k1, the second mass is connected to another fixed wall with k3, and both masses are connected to each other with . Using the theory of small oscillations, what is the essential step in determining the normal modes and frequencies of this system?
1
Compute the potential energy of the system and linearize it around the equilibrium positions of the masses to determine the stiffness matrix.
2
Analyze the system by treating each mass independently without considering the influence of the other mass to simplify the calculations.
3
Focus on non-linear terms in the potential energy expansion to account for large displacements from equilibrium.
4
Ignore the kinetic energy since the masses are assumed to oscillate with very small amplitudes.
5
Question Not Attempted