Transcription of LECTURE 14: DEVELOPING THE EQUATIONS OF MOTION FOR …
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LECTURE 14: DEVELOPING THE EQUATIONS OF MOTION FOR …
211 LECTURE 14: DEVELOPING THE EQUATIONS OFMOTION FOR TWO-MASS VIBRATION EXAMPLESF igure a. Two-mass, linear vibration system with springconnections. b. Free-body diagrams. c. Alternative ( )( ) EQUATIONS of MOTION Assuming: The connecting spring is in tension, and the connecting spring-force magnitude is . From figure :with the resultant differential EQUATIONS : EQUATIONS of MOTION Assuming: The spring is in compression, and the connecting-spring forcemagnitude is . From figure :Rearranging these differential EQUATIONS gives Eqs.
Simple -pendulum equations of motion, Equations of motion for mass m2: We now have two additional unknowns . Kinematics from figure 3.54: Differentiating with respect to time gives: Differentiating again gives:
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