Question

In: Math

The output of an engineering system as a function of position (x) is modeled by the...

The output of an engineering system as a function of position (x) is modeled by the differential equation y'' + 9y = 5cos(2x) - 10sin(2x), where y = f(x), y(π/2) = 2, and y'(π/2) = 6. Solve this differential equation to obtain an expression for y as a function of x (i.e., to obtain the function y(x)).

Solutions

Expert Solution



Related Solutions

A bicyclist is riding on a path modeled by the function f(x) = 0.07x, where x...
A bicyclist is riding on a path modeled by the function f(x) = 0.07x, where x and f(x) are measured in miles (see figure). Find the rate of change of elevation at x = 5.
x[n] is the input of a system and y[n] is the output of the system. The...
x[n] is the input of a system and y[n] is the output of the system. The relationship between the input and output is the following: y[n] = x[n]u[n+1] a) Is the system memoryless? Just yes or no is sufficient. b) Is this system causal? Just yes or no is sufficient. c) Is the system linear? Just yes or no is sufficient. d) Is the system time invariant? Justify. e) Is the system BIBO stable? Justify. f) Is the system invertible?...
Determine the output of the following program: var x; function bar() { writeln(x); } function foo()...
Determine the output of the following program: var x; function bar() { writeln(x); } function foo() { var x; x = 3; bar(); } function oof() { var x; x = 7; foo(); } x = 5; oof(); (a) if the static scoping rule is used? What is the reason?. (b) if the dynamic scoping rule is used? What is the reason?.
With the use of a phase shift, the position of an object may be modeled as...
With the use of a phase shift, the position of an object may be modeled as a cosine or sine function (as a function of time). If given the option, which function would you choose (Note: this is an open-ended question; there is no wrong answer; just be sure to explain your choice)? Assuming zero phase shift, if you are using a sine function to model the position of an object, what are the initial conditions of the oscillator---that is,...
With the use of a phase shift, the position of an object may be modeled as...
With the use of a phase shift, the position of an object may be modeled as a cosine or sine function (as a function of time). If given the option, which function would you choose (Note: this is an open-ended question; there is no wrong answer; just be sure to explain your choice please)? Assuming zero phase shift, if you are using a sine function to model the position of an object, what are the initial conditions of the oscillator---that...
write a Matlab function file to solve system Ax=b by using the output of the function...
write a Matlab function file to solve system Ax=b by using the output of the function lufac2a your function should have inputs f=matrix return from lufac2a, piv=array return by lufac2a and b=right hand side of your system.the only output for your system should be x guideline 1.use the column access for the matrix entries 2. do not create any other matrix in your function-get your data directly from the matrix passed into your function 3.do not use Matlab command designed...
Consider the following production function: x = f(l,k) = lb kb where x is the output,...
Consider the following production function: x = f(l,k) = lb kb where x is the output, l is the labour input, k is the capital input, and b is a positive constant. Suppose b < 1/2. (a) Set up the cost minimization problem and solve for the conditional labour and conditional capital demand functions. Let w and r be the wage rate and rental cost of capital respectively. (b) Using your answer in (a), derive the cost function and simplify...
For the following exercises, use this scenario: The population P of a koi pond over x months is modeled by the function P(x) = 68/1 + 16e−0.28x.
For the following exercises, use this scenario: The population P of a koi pond over x months is modeled by the function P(x) = 68/1 + 16e−0.28x.Use the intersect feature to approximate the number of months it will take before the population of the pond reaches half its carrying capacity.
The resistance R of a tungsten wire as a function of temperature can be modeled with...
The resistance R of a tungsten wire as a function of temperature can be modeled with the equation R=R0*[1+α(T-T0 ) whereR0 is the resistance corresponding to temperature T0, and α is the temperaturecoefficient of resistance. Determine R0and α such that the equation will best fit the following data (Use linear regression curve fitting). Take T0 = 20°C. T=[20 100 180 260 340 420 500] R=[500 676 870 1060 1205 1410 1565] After enter below codes it gives an error function...
Consider a system with the input/output relationship y(t) = x(t)cos(15πt). (a) Is this system (i) linear,...
Consider a system with the input/output relationship y(t) = x(t)cos(15πt). (a) Is this system (i) linear, (ii) causal, (iii) stable, (iv) memoryless, (v) time-invariant, and (vi) invertible. Justify each answer with a clear mathematical argument. (b) Find the Fourier Transform Y (f) of y(t) in terms of the transform X(f) of x(t). Repeat problem (2) for the system with the input-output relationship y(t) =R1 τ=0(1−τ)2x(t−τ)dτ.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT