Solving Problems in Dynamics and Vibrations Using MATLAB ...

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20 Assignment Plot the response of a forced system given by the equation m x+ c x+ kx = For ξ = {0, 0.1 0.25, 0.5, 0.75, 1.0}. .. . f sinω Take m = 5 kg; k = 1000 N/m; f = 50 N; ω = 4ω n , x(0) = 5 cms; t ẋ (0) = 0. Develop a plot for the solutions corresponding to the seven ξ values and comment on the plots obtained.
21 2. Simple Pendulum θ l m Example Compute and plot the linear response of a simple pendulum having a mass of 10 grams and a length of 5 cms. The initial conditions are θ (0) = 90° and θ (0) = 0 Also compare the generated plot with the nonlinear plot. Solution The differential equation of motion for the simple pendulum without any damping is given by . .. g θ = ( − ) sinθ l If we consider the system to be linear, i.e., for small angles, sinθ =θ So the linearized version of the above non-linear differential equation reduces to .. g θ = ( − )θ l The above equation is a second order, constant-coefficient differential equation. In order to use MATLAB to solve it, we have to reduce it to two first order differential equations as MATLAB uses a Runge-kutta method to solve differential equations, which is applicable only for first order differential equations. Let θ = y(1) . θ = y(2)
Page 1 and 2: Solving Problems in Dynamics and Vi
Page 3 and 4: 3 An Introduction to MATLAB Purpose
Page 5 and 6: 5 x + 2y = 6 x − y = 0 There are
Page 7 and 8: 7 p = ‘x + 2*y = a + 6’ q = ‘
Page 9 and 10: 9 Suppose one wants to change the c
Page 11 and 12: 11 1. Spring Mass Damper System - U
Page 13 and 14: 13 MATLAB Code In order to apply th
Page 15 and 16: 15 Assignment Solve for six cycles
Page 17 and 18: 17 For our convenience, put x = y (
Page 22 and 23: 22 When the values of ‘theta’ a
Page 25 and 26: 25 Assignment a) Compute and plot t
Page 27: 27 tspan=[0 2] y0=[0;0] [t,y]=ode45
Page 30 and 31: 30 4. Trajectory Motion with Aerody
Page 33 and 34: 33 Assignment Solve the following d
Page 35 and 36: 35 Open a new m-file and type the f
Page 37 and 38: 37 Assignment a) Solve the followin
Page 39 and 40: 39 y0=[0.5233;0]; [t,y]=ode45('tofr
Page 41 and 42: 41 7. A bar supported by a cord Der
Page 43 and 44: 43 MATLAB Code In this type of a pr
Page 45: 45 tspan=[0 30] y0=[0.5233;0;1.0467
Page 50 and 51: 50 8. Double Pendulum Derive the go
Page 52 and 53: 52 yp(1)=y(2); yp(2)=-(w1+w2)*sin(y
Page 55 and 56: 55 Assignment 1.) For the double pe
Page 57 and 58: 57 2 ⎡−ω [ M ] + [ K] ω[ C]
Page 59: 59 figure(1) plot(f,x(1,:));grid xl
Page 63 and 64: 63 10. A Three Bar Linkage Problem
Page 65: 65 xlabel('alpha') ylabel('gamma do
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70 11. Slider-Crank Mechanism Examp
Page 72:
72 To calculate the angular acceler
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77 12. A Bar supported by a wire an
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79 end To store the right hand side
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81 t1=t'; figure(3) plot(t1,theta);
Page 85 and 86:
85 The above model involves second
Page 87 and 88:
87 l=1; L=1.5; m=5; M=5; g=9.81; w=
Page 91 and 92:
91 Assignment: Three bar linkage as
Page 93 and 94:
93 where ⎥ ⎥ ⎥ ⎥ ⎥ ⎥
Page 95 and 96:
95 ⎡kx1 ⎤ ⎢ ⎥ ⎢ 0 ⎥ ⎢
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97 m = 0.002; k = 175000; M1 = m*ey
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99 cnt = cnt +1; end end end % To p
Page 101 and 102:
101 plot(vect3(:,i),c(i)) hold on;
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103
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