EA3_forcedosc - EA3: Systems Dynamics Mechanical Systems...

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EA3: Systems Dynamics Mechanical Systems Sridhar Krishnaswamy 22 VI.5 FORCED OSCILLATIONS OF A SPRING-MASS SYSTEM Let us return to the spring-mass system. But now let us suppose that a force source acts at one end of the mass as shown. Furthermore let us say that the spring-mass system is initially quiescent (spring is unstretched and mass has zero velocity at time zero). Figure 6.15 : Spring-mass system with external forcing State variables: X = r sp 1 v m 2 It should be easy for you to show that the state equation for this system is now given by: ˙ r sp 1 ˙ v m 2 = 0 1 - K 1 m 2 0 r sp 1 v m 2 + 0 F 3 ( t ) m 2 which I will write as: ˙ X = A X + F where F is called the source term. In prinicple, it should not be any harder to solve the above system of equations using our MATLAB m-files, but I will need to modify my rate function file (rate_fn.m) to another one (frate_fn.m) which can handle the additional source term on the right side. I have done this for you. %EA3 %%--------------------------------------------------------- %%Example: Spring-mass-system with a harmonic force source %%--------------------------------------------------------- clear all; close all; global A F; %share these with function frate_fn which computes Xdot=AX+F %% %%System parameters K1 = 40; %element 1 - spring m2 = 10; %element 2 - mass wf = 2.0001; %frequency of force source function F3(t)=F0*sin(wf*t) F0 = 1; %force source amplitude 1 2 3 1: K 1 2: m 2 F 3 (t)=F o sinw f t
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EA3_forcedosc - EA3: Systems Dynamics Mechanical Systems...

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