Advanced Mathematics and Mechanics Applications Using by David Halpern, Howard B. Wilson, Louis H. Turcotte

By David Halpern, Howard B. Wilson, Louis H. Turcotte

Considering the fact that its creation in 1984, MATLAB's ever-growing recognition and performance have secured its place as an industry-standard software program package deal. The common, interactive surroundings of MATLAB 6.x, which incorporates a high-level programming language, flexible pix services, and abundance of intrinsic services, is helping clients specialise in their purposes instead of on programming error. MATLAB has now leapt some distance sooner than FORTRAN because the software program of selection for engineering functions.

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Extra resources for Advanced Mathematics and Mechanics Applications Using MATLAB, Third Edition

Example text

The nature of F (x) implies that the motion has a period of 2l/a. Waves striking the boundary are reßected in inverted form so that for any time y(x, t + l/a) = −y(x, t). 67, 1], yd = [0, 0, −1, 0, 0]. The program reads the wave speed, the string length, and data points specifying the initial deßection. The solution is evaluated for a range of x, t values. 10, which is a three-dimensional plot of traces of the string deßection for a sequence of times. 33. 25. Finally, a function to animate the solution over two motion cycles illustrates how the initial deßection splits, translates, and reßects from the boundaries.

9 shows the Þnal position of the mass and the applied force at the end of the chosen motion cycle. 9: Block Sliding On a Plane with Viscous Damping © 2003 by CRC Press LLC 30 Program smdplot 1: 2: 3: 4: 5: 6: 7: 8: 9: 10: 11: 12: 13: function [t,X,m,c,k,f1,f2,w,x0,v0]= smdplot(example) % % [t,X,m,c,k,f1,f2,w,x0,v0]= smdplot(example) % ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ % This function plots the response and animates the % motion of a damped linear harmonic oscillator % characterized by the differential equation % m*x’’+c*x’+k*x=f1*cos(w*t)+f2*sin(w*t) % with initial conditions x(0)=x0, x’(0)=v0.

Among the Þve properties, © 2003 by CRC Press LLC only torsion, τ , depends on R (t). The pertinent formulas are R (t) ˆ = R (t) × R (t) , B Tˆ = |R (t)| |R (t) × R (t)| ˆ =B ˆ × Tˆ , κ = |R (t) × R (t)| N |R (t)|3 and τ= ˆ · R (t) B . |R (t) × R (t)| When the independent variable t means time we get V = velocity = ds dR dR = = v Tˆ dt dt ds where v is the magnitude of velocity called speed. Differentiating again leads to dV dv ˆ ˆ = acceleration = T + κv 2 N dt dt so the acceleration involves a tangential component with magnitude equal to the time rate of change of speed, and a normal component of magnitude κv 2 directed toward the center of curvature.

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