EA3: Systems Dynamics II Dynamics of Particles
Dynamics of Particles
II. 1. Motion of a particle: In EA2, you encountered the basic concepts of mechanics. You learnt how to solve for the motion of rigid particles under the action of external forces

EA3: Systems Dynamics
Mechanical Systems
VI.4 DAMPED OSCILLATIONS Consider the {spring-damper}-mass system shown. 1:K1
3 1 2:C2 Figure 6.11: Damped spring-mass system There is a slight complication to this system. Is this one-dimensional? Actually

EA3: Systems Dynamics V IMPULSE AND MOMENTUM
Momentum Methods
V.1 Linear Impulse: Newton's laws say that if a net force F acts on a body, then: dp (5.1) F= dt where p = mv is the linear momentum of the body, where m is the mass and v is the velocit

EA3
Friction
Friction
Friction is a force that acts to oppose the sliding motion of two dry bodies in contact. It always acts in opposition to actual or potential sliding motion. The root cause of friction has to do with asperities (bumps) on rough

EA3: Systems Dynamics
Electrical Systems
TRANSMISSION LINES Consider a length of coaxial cable that connects your Cable TV port to your TV input. This cable, and other similar things such as your data transmission line, can all be modeled as a bunc

EA3: Systems Dynamics
Better algorithms for numerical integration
Better Algorithms for Numerical Integration Let us consider a general differential equation involving some function y(t): dy = f (y) dt y(0) = y0 .
DE:
(1)
along with the initial

EA3: Systems Dynamics RLC-CIRCUIT: TONE CONTROL
Electrical Systems
Figure: A graphics equalizer (courtesy EA3 hyperbook) Most of you have used a graphics equalizer to alter the bass and treble of music that for some reason you do not like to hear t

EA3: Systems Dynamics
Spring-block oscillator
III The spring-block oscillator Let us consider a simple spring-block system in the absence of any friction or air drag. We assume that the block is rigid and has mass, and the spring is massless but is

EA3: Systems Dynamics
Mechanical Systems
VI SYSTEMS DYNAMICS MECHANICAL SYSTEMS VI.1 Modeling Mechanical Systems: We have already looked at some simple one-dimensional mechanical systems involving springs and blocks:
Spring constant K (N/m) mass

EA3: Systems Dynamics
Mechanical Systems
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 spri

EA3: Systems Dynamics IV Work and Energy
Work and Energy
Newton's laws provide us the tools necessary to track the motion of a body under the action of external forces. We have seen how to go about that for several situations, some of which were am

EA3: Systems Dynamics
Electrical Systems
VIII. SYSTEMS DYNAMICS Electrical Domain Let us now delve into some simple electrical systems. Once again, we will adopt a systems approach here and infer a lot about the behavior of electrical systems by a

EA3: Systems Dynamics
Electrical Systems
VIII.2.1 LC-Oscillator Circuit: At time t=0, the switch is closed. A current begins to flow and the capacitor charges. How do the voltages and currents in the circuit change with time?
iC
+ + VB i + -
C
i