Determine the value of w for which the following harmonic oscillator (left hand side), subjected to the forcing function (right hand side), experiences pure resonance (i.e. the response function experiences unbounded growth in amplitude): (a) 3. +7.x = cos (wt) d'x dt² Pure resonance: 13 (b) 3. +2.x=2.sin (w t) + 2. cos (w t) d²x dt² Pure resonance:

Q: Problem 6 This extreme value problem has a solution with both a maximum value and a minimum value.…

A:

Q: Solve the differential equation: (D² + 1)y = tan x

A:

Q: Approximate the area of the region enclosed by y = -x² + 4x and x-axis using trapezoidal rule with 8…

A: Given y = -x2 + 4x h = b-aNh = 4-08 = 0.5

Q: à = (2, -1) and b = (1,3). Represent a + b by using the parallelogram method.

A:

Q: 4. Show that if A is closed in Y and Y is closed in X, then A is closed in X. Verify it and make…

A:

Q: Consider a system which is modelled by where F(t) represents where A and B are constants of…

A: Consider the given system u''+16u=Ft

Q: [MO31] Find the Fourier series of,

A: Given,           f(x)=0-2<x<-1-x-1<x<11   1<x<2

Q: Find area of the region bounded by x² + y² = 42, 9y = -10x and 14y 5x where y > 0. Leave your answer…

A: Given that,A region is bounded by x2+y2=42, 9y=-10x and 14y=5x, y≥0.The area of the above region is…

Q: Example 10.27. Find an approximate series solution of the simultaneous equations dx/dt = xy + 2t,…

A: Here, we need to find approximate series solution.

Q: he offers two products, turntables and cassette players. makes a profit of P300.00 on each…

A: Given that Garry Mornes assembles stereo equipment for sale in his shop he offers two products,…

Q: Let x = [1,1], y = [1,1] € R² and let f: R² ⇒ R² with f(z) = 2₁.x + 22.y for any z = [21, 22] € R².…

A:

Q: ᴸᵉᵗ µ ᵇᵉ ᵗʰᵉ ᶜᵒᵘⁿᵗⁱⁿᵍ ᵐᵉᵃˢᵘʳᵉ ᵒⁿ ᴺ. ᴸᵉᵗ ᴱ¹ ⁼ {¹, ², ⁴, ⁵} ᵃⁿᵈ ᴱ² ⁼ {ˣ | ˣ ⁱˢ ᵃ ᵖᵒˢⁱᵗⁱᵛᵉ ⁿᵃᵗᵘʳᵃˡ…

A: Given : It is given that  μ is a counting measure on ℕ  with  E1 = 1, 2, 4, 5  and,…

Q: Using two intervals of Simpson's 1/3 rule, an estimate value of f(x) dx is 11.51. The estimate of…

A:

Q: How many strings of three decimal digits (each digit can be 0-9) do not contain the same digit three…

A: Solution :-

Q: Find the eigenvalues of the triangular or diagonal matrix. (Enter your answers as a comma-separated…

A:

Q: Given, dr = b(cosedr+rsinėdė);r(π) = 1. Find (1) 1 1+b O 1+b 2 1 1+b O b -(1-b) 1+b

A: We have to find the value of rπ2

Q: H-w.4 Find the volumes for the following solids whose heights are defined by E (x,y) and bases are…

A: Volume bounded by xy-plane plane.

Q: Determine whether the DE has homogeneous coefficients. If so, find the implicit solution.…

A:

Q: II. Find Do not simplify your answers. dy dx tan-¹(cosh.r) 2. y= (sin²x) (sech x)sec z [use…

A:

Q: 8. Iff and g are differentiable at xo such that f(xo) g(xo), prove that each of the functions h =…

A: (8) Given that f and g are differentiable at x0 such that fx0≠gx0.Also h=minf,g and H=maxf,g. To…

Q: Given the family C[0, 1] of continuous functions ƒ [0, 1] → R, and the norm ||f|| = sup |f(x)]. x=…

A:

Q: Identify and draw a sketch of the surface [(x-2)] ^2/9+ [(y-3)] ^2/4- [(z-1)] ^2/36=1 O elliptic…

A: Equation for elliptic hyperboloid of one sheet with center (0,0,0) is  x2a2+y2b2-z2c2=1

Q: Consider the matrix A = - (²-2) (a) Compute the eigenvalues and the corresponding eigenve (b) Let v…

A:

Q: .Using 1 - node Gaussian integration, we have f f(x) dx wif(x₁). What is the value of x₁ ? b-a (c)…

A:

Q: Prove that the subgroup {o ES5o (5) = 5} of S5 is isomorphic to $4.

A: The given question is related with abstract algebra. We have to the subgroup σ ∈ S5 | σ5 = 5 of S5…

Q: Problem : Consider the following van der Pol oscillator: x+µ(x² − 1)x + x = 0 a) Show that the…

A: As per the question we are given a van der Pol oscillator, and we have to find its state space…

Q: J 2 3 ув-у'-6y=0 y" +2y'= у"+3y"-4y'=0 О

A: According to our guidelines, we are supposed to answer only first three subparts.Kindly repost other…

Q: 15-46. Graphing functions Use the guidelines of this section to make a complete graph of f. 31.…

A: We have to draw the graph of given function.

Q: Find the divergence and curl for the following vector fields. Describe the characteristics of the…

A:

Q: Use Cramer's rule to solve the linear system of equations; 2x2 + 5x3 = 1 2x₁ + x₂ + x3 = 1 3x₁ + x₂…

A: Given equations are 2x2 + 5x3 = 12x1+x2+x3 = 13x1+x2 = 2

Q: Show that the equation 2²y Əy +2k 2²y 6x² ax² 1 2² Ət possesses solutions of the form X 00 kt Σ c,…

A:

Q: 1. Let k € N. Determine all values of a such that Sink converges. an R

A: Suppose k∈ℕ and consider the series: ∑n=0∞nkanTo find: All values of a such that ∑n=0∞nkan…

Q: Is the cobb-douglas function strictly concave when a1 +a2 <1 when

A:

Q: ind the function(x), such that f'(x)= In (3x) X ƒ(1)-1. "

A: Function of a variable x

Q: A recent college graduate borrows $150,000 at an interest rate of 6% to purchase a condominium.…

A: Please find step by step solution below:

Q: Solve the and many differential equation d/an (D²+1) {D-5)³y=0;

A: Given differential equation:D2+1D-53y=0To find: General solution of the differential equation.

Q: a Verity. functions and form. a basis of solutions of the given ODE? (b) Solve the IVP of that given…

A:

Q: 3. fe2x+Inx² sin x² dx = = 2x -+√e²x cos x² dx

A:

Q: Q.3: Solve the following set of four linear equations using Gauss-Seidel iteration method; Continue…

A:

Q: Find the volumes for the following solids whose heights are defined by Z(x,y) and bases are the…

A: Volume bounded by xy-plane plane.

Q: Use the geometric method to find the eigenvalue(s) and corresponding eigenspace(s) of A. 1 0 A = -…

A:

Q: Use the second Taylor polynomial P₂(x) for f(x) = x² + ln(1 + x) about æ = 0 and evaluate ƒ ƒ(x)dx.…

A: Given function is fx=x2+ln1+x. We have to evaluate  ∫01fxdx by using the second Taylor polynomial…

Q: Reduce to the form x + yi: logsin (-i+2) 2 40eπi

A: We have to reduce logsin-i+240e23πi to the form x+iy

Q: Which of the following series is converge or diverge - ΣΤ' ,0.7777777777777 n2 n=1 . Σ{} 27

A:

Q: 2. Use Squeeze Theorem to evaluate lim sin(sinh x) csch z. 8118

A: 2) use squeeze theorem to evaluate limx→-∞sinsinhx cschx it is known that  -1≤sinsinhx≤1 implies,…

Q: Write the following English sentences in symbolic form- 1. If I will go to Australia, then I will…

A:

Q: 10 inches 6 inches 18 inches Using the dimensions from the previous item, find the rate of change in…

A: Given total surface area formula of rectangular solid SA=2lw+2lh+2wh   ......(1) where l,w,h are the…

Q: Let x₁, x₂ denote the variables for the two-dimensional data summarized by the covariance matrix,…

A: As per the question we are given a covariance matrix along with ots eigenvalues &amp; eigenvectors,…

Q: ind the area under the graph of the function y=2-x-x² over the interval[-2.1]

A:

Q: C.W. Churchman once said that "Mathematics...tends to lull the unsuspecting that he who thinks…

A: No. Normally the best models of quantitative analysis are not mathematically complex. The reason is…