- #1

LCSphysicist

- 636

- 153

- Homework Statement:
- ALl below

- Relevant Equations:
- ALl below

We need to find the normal modes of this system:

Well, this system is a little easy to deal when we put it in a system and solve the system... That's not what i want to do, i want to try my direct matrix methods.

We have springs with stiffness k1,k2,k3,k4 respectively, and block mass m1, m2, m3

And we need to annul the determinant of
, not just, i supposed the displacement Z as complex, so we need real angular frequencies.

To mount the matrix K, we need to know all Kij, being Kij the spring stiffness equivalent if we move just block j and analyze the motion of block i, j can be equal i.

So making all the things, we end with:

Apparently this is wrong, i found just complex w, what is the problem?

Well, this system is a little easy to deal when we put it in a system and solve the system... That's not what i want to do, i want to try my direct matrix methods.

We have springs with stiffness k1,k2,k3,k4 respectively, and block mass m1, m2, m3

And we need to annul the determinant of

To mount the matrix K, we need to know all Kij, being Kij the spring stiffness equivalent if we move just block j and analyze the motion of block i, j can be equal i.

So making all the things, we end with:

Apparently this is wrong, i found just complex w, what is the problem?