Homework Answers
The steady state response is w=3. Because from w=3.01 to w=3, there is almost no change in y values.
From the graph, as w decreases from 4 to 3 curve moves upwards and then gradually remains same. So w=3.01 and w=3 plots are superimposed here.
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help with matlab
2. Consider the undamped oscillator equation dy + 9y = cos(wt) dt2 y(0)...
QUESTION 6 please help MATLAB to and you 5. MATLAB can also solve second order equations...
QUESTION 6 please help
MATLAB
to and you 5. MATLAB can also solve second order equations symbolically using the Symbolic packages. The help page https://www.mathworks.com/help/symbolic/solve-a-single-differential-equation. html#f1-11214 shows examples of how this works. Code this up for the same equation and see if you get the same answer. If you don't (and you probably won't), try simplifying the answer after you get it to see if it matches then. Note: You'll need to define the symbolic function y(t) here in order...
Problem 1.Consider the harmonically forced undamped oscillator described by the following ODE:mx′′+kx=F0cosωt, k >0, m >0,...
Problem 1.Consider the harmonically forced
undamped oscillator described by the following ODE:mx′′+kx=F0cosωt,
k >0, m >0, ω >0, F0∈R.
Problem 1. Consider the harmonically forced undamped oscillator described by the following ODE: mx" + kx = Fo cos wt, k > 0, m > 0,w > 0, F0 E R. (1) a) Suppose wa #k/m. Find the general solution of the ODE ). b) Consider the initial value problem of the ODE () with initial conditions x(0) = 0 and...
In MatLab: 1. For the following differential equation: *x = Fo cos(wt) x( 0) = 0,...
In MatLab:
1. For the following differential equation: *x = Fo cos(wt) x( 0) = 0, find Set Fo 1 and w = 0.9. Starting with zero initial conditions, i.e. x(0) the solutions x and x for 0 sts 100. Plot xt)
(1 point) Consider the initial value problem d2y dy 8 +41y8 cos(2t), dt dy (0) y(0) = -2 -6 dt dt2 Write down the Lapla...
(1 point) Consider the initial value problem d2y dy 8 +41y8 cos(2t), dt dy (0) y(0) = -2 -6 dt dt2 Write down the Laplace transform of the left-hand side of the equation given the initial conditions (sA2-8s+41)Y+2s-18 Your answer should be a function of s and Y with Y denoting the Laplace transform of the solution y. Write down the Laplace transform of the right-hand side of the equation (-8s+32)/(sA2-8s+20) Your answer should be a function of s only...
3) Consider the following vibrating system u" (1/4) 2u 2 cos (wt), u (0) 0, (0) 2 (a) Find transient and steady states of solution (b) Find the amplitude R of the steady state solution in terms o...
3) Consider the following vibrating system u" (1/4) 2u 2 cos (wt), u (0) 0, (0) 2 (a) Find transient and steady states of solution (b) Find the amplitude R of the steady state solution in terms of w and plot R versus w; (c) Find Rmax and wmax
3) Consider the following vibrating system u" (1/4) 2u 2 cos (wt), u (0) 0, (0) 2 (a) Find transient and steady states of solution (b) Find the amplitude R of...
#40 a-f B-A. (B+A ". Beats slation Recall the identity cos A-cos Be2-2A)sin(-2A) a. Show that 0-10,a, . 9 and (ii)o_10,us2toverify the identity. In which case do you see Gaph the functions on...
#40 a-f
B-A. (B+A ". Beats slation Recall the identity cos A-cos Be2-2A)sin(-2A) a. Show that 0-10,a, . 9 and (ii)o_10,us2toverify the identity. In which case do you see Gaph the functions on both sides of the equation in part (a) with (i) beats? b. 40 Analysis of the forced damped oscillation equation Consider the equation my"+ey'+ky Fo cos wof, which oscillator. Assume all the parameters in the equation are positive. a. Explain why the solutions of the homogeneous equation...
Consider the equation for the charge on a capacitor in an LRC circuit da + dt2...
Consider the equation for the charge on a capacitor in an LRC circuit da + dt2 +79 = E dt which is linear with constant coefficients. , and find the auxiliary equation (using m as your First we will work on solving the corresponding homogeneous equation. Divide through the equation by the coefficient on variable) = 0 which has roots The solutions of the homogeneous equation are Now we are ready to solve the nonhomogeneous equation + 16 + 634...
Problem Thre: 125 points) Consider the following initial value problem: dy-2y+ t The y(0) -1 ea dt ical solution of the differential equation is: y(O)(2-2t+3e-2+1)y fr exoc the differential equat...
Problem Thre: 125 points) Consider the following initial value problem: dy-2y+ t The y(0) -1 ea dt ical solution of the differential equation is: y(O)(2-2t+3e-2+1)y fr exoc the differential equation numerically over the interval 0 s i s 2.0 and a step size h At 0.5.A Apply the following Runge-Kutta methods for each of the step. (show your calculations) i. [0.0 0.5: Euler method ii. [0.5 1.0]: Heun method. ii. [1.0 1.5): Midpoint method. iv. [1.5 2.0): 4h RK method...
Use the attached Matlab code as a basis to solve the following ordinary differential equation usi...
Question 1
QUESTION 2
Use the attached Matlab code as a basis to solve the following ordinary differential equation using Euler's method, with timestep of 0.1, from t-0to t-100. d)0) -0 - sin (5vt cos(у Plot y versus t from t=0 to t=100. How many local maxima are on this interval(do not include end points). Be careful to count them all! Answer should be an integer 1 w% Matlab code for the solution of Module 2 3 dt-9.1; %dt is...
Please help solve this, using the equation to get through the problem. Additional information: where the...
Please help solve this, using the equation
to get through the problem.
Additional information:
where the initial position
, the initial speed
The above differential equation can also be written as:
If
, there is light damping where the solution has the form ( where r
and w are two positive constants)
or
If
there is heavy damping where,
where
and
are two positive constants
If
there is critical damping where,
where r is a positive constant
d'y dy ma...
QUESTION 6 please help
MATLAB
to and you 5. MATLAB can also solve second order equations symbolically using the Symbolic packages. The help page https://www.mathworks.com/help/symbolic/solve-a-single-differential-equation. html#f1-11214 shows examples of how this works. Code this up for the same equation and see if you get the same answer. If you don't (and you probably won't), try simplifying the answer after you get it to see if it matches then. Note: You'll need to define the symbolic function y(t) here in order...
Problem 1.Consider the harmonically forced
undamped oscillator described by the following ODE:mx′′+kx=F0cosωt,
k >0, m >0, ω >0, F0∈R.
Problem 1. Consider the harmonically forced undamped oscillator described by the following ODE: mx" + kx = Fo cos wt, k > 0, m > 0,w > 0, F0 E R. (1) a) Suppose wa #k/m. Find the general solution of the ODE ). b) Consider the initial value problem of the ODE () with initial conditions x(0) = 0 and...
In MatLab:
1. For the following differential equation: *x = Fo cos(wt) x( 0) = 0, find Set Fo 1 and w = 0.9. Starting with zero initial conditions, i.e. x(0) the solutions x and x for 0 sts 100. Plot xt)
(1 point) Consider the initial value problem d2y dy 8 +41y8 cos(2t), dt dy (0) y(0) = -2 -6 dt dt2 Write down the Laplace transform of the left-hand side of the equation given the initial conditions (sA2-8s+41)Y+2s-18 Your answer should be a function of s and Y with Y denoting the Laplace transform of the solution y. Write down the Laplace transform of the right-hand side of the equation (-8s+32)/(sA2-8s+20) Your answer should be a function of s only...
3) Consider the following vibrating system u" (1/4) 2u 2 cos (wt), u (0) 0, (0) 2 (a) Find transient and steady states of solution (b) Find the amplitude R of the steady state solution in terms of w and plot R versus w; (c) Find Rmax and wmax
3) Consider the following vibrating system u" (1/4) 2u 2 cos (wt), u (0) 0, (0) 2 (a) Find transient and steady states of solution (b) Find the amplitude R of...
#40 a-f
B-A. (B+A ". Beats slation Recall the identity cos A-cos Be2-2A)sin(-2A) a. Show that 0-10,a, . 9 and (ii)o_10,us2toverify the identity. In which case do you see Gaph the functions on both sides of the equation in part (a) with (i) beats? b. 40 Analysis of the forced damped oscillation equation Consider the equation my"+ey'+ky Fo cos wof, which oscillator. Assume all the parameters in the equation are positive. a. Explain why the solutions of the homogeneous equation...
Consider the equation for the charge on a capacitor in an LRC circuit da + dt2 +79 = E dt which is linear with constant coefficients. , and find the auxiliary equation (using m as your First we will work on solving the corresponding homogeneous equation. Divide through the equation by the coefficient on variable) = 0 which has roots The solutions of the homogeneous equation are Now we are ready to solve the nonhomogeneous equation + 16 + 634...
Problem Thre: 125 points) Consider the following initial value problem: dy-2y+ t The y(0) -1 ea dt ical solution of the differential equation is: y(O)(2-2t+3e-2+1)y fr exoc the differential equation numerically over the interval 0 s i s 2.0 and a step size h At 0.5.A Apply the following Runge-Kutta methods for each of the step. (show your calculations) i. [0.0 0.5: Euler method ii. [0.5 1.0]: Heun method. ii. [1.0 1.5): Midpoint method. iv. [1.5 2.0): 4h RK method...
Question 1
QUESTION 2
Use the attached Matlab code as a basis to solve the following ordinary differential equation using Euler's method, with timestep of 0.1, from t-0to t-100. d)0) -0 - sin (5vt cos(у Plot y versus t from t=0 to t=100. How many local maxima are on this interval(do not include end points). Be careful to count them all! Answer should be an integer 1 w% Matlab code for the solution of Module 2 3 dt-9.1; %dt is...
Please help solve this, using the equation
to get through the problem.
Additional information:
where the initial position
, the initial speed
The above differential equation can also be written as:
If
, there is light damping where the solution has the form ( where r
and w are two positive constants)
or
If
there is heavy damping where,
where
and
are two positive constants
If
there is critical damping where,
where r is a positive constant
d'y dy ma...
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