{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

lecture1010

# lecture1010 - ME 563 Mechanical Vibrations Lecture#10...

This preview shows pages 1–6. Sign up to view the full content.

ME 563 Mechanical Vibrations Lecture #10 Single Degree of Freedom Free Response

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Free Response 1 When solving the homogeneous equation of motion (forcing function = 0), we are finding the free response. One way to solve for the free response is as follows: - Identify the initial conditions on all the states - Assume a solution of the form x(t)=Ae st
Disc on An Incline 2 Consider the disc on an incline with no forcing function: Recall x d is called the dynamic displacement. If we make a solution of the form, , we obtain:

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Characteristic Equation 3 The only solutions that satisfy the equation of motion that are not trivial ( A =0) must also satisfy the characteristic equation : The solution to the homogeneous equation are then written as follows: Roots, poles, modal frequencies Because the equation is linear, the solutions superimpose…
Initial Conditions 4 It is important to note that the modal frequencies of the system are only a function of the mass, damping, and stiffness

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 17

lecture1010 - ME 563 Mechanical Vibrations Lecture#10...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online