The periodic outer force F = sin wt is applied to the mass-spring system from Task 2. The equation becomes y" = -3y – cy' + sin wt, c > 0. (a) Find a periodic solution of this equation in the form y(t) = a cos wt + b sin wt (the answer will depend on c, w). Prove that the amplitude of this solution is ((3 – w²)² + c²w²)-0.5. (b) Fix c (you may assume that c is small) and find w = wmaz > 0 such that the amplitude of this periodic solution reaches its maximum at w. Comment: you will see that for larger c, the amplitude monotonically decreases as w increases, and thus there is no maximum point wmaz > 0. Hint: you may wish to denote v = w when searching for the maximum, but remember that v > 0. (c) For w = 1,c = 2, write out the general solution of this equation (cv. Task 2a) and show that all solutions tend to the periodic solution as t → +00.

Q: Let E denote the region bounded by the plane 2x + y+ z= 2 and the first octant. Let g(x, y, z) be a…

A: To find the limit of integration of the below integral. ∫∫E∫gx,y,zdV=∫∫∫gx,y,zdzdydx The region E is…

Q: How do you solve this problem?

A:

Q: Find dy/dx by implicit differentiation. y sin( x) = -x sin

A:

Q: Find a simple, closed form for the generating function of the sequence defined by an = n².

A:

Q: Solve the second-order equation y" + 2y' – 3y = 9x with initial condition y(0) = 0, y' (0) = 0.

A:

Q: What is the measure of ZDC'?

A:

Q: Prove that the number of partitions of n into at most k parts is equal to that of partitions of n +…

A: given , number of partitions of n into k parts  we have to prove that , partitions of number n + k…

Q: How do you solve this problem?

A: We are given the system of differential equation,                          . We are also given the…

Q: How do you solve this?

A: Given the differential equation is,

Q: Use the substitution v(x) = y(x)/x to solve the differential equation dy x² + 2y? dx 2xy

A:

Q: How do you solve this problem?

A:

Q: A stone is dropped into a well, and the time it takes to hear the splash is 3.0 seconds. Find the…

A: NOTE: Refresh your page if you can't see any equations. . A stone is dropped into a well of depth d,…

Q: REMEMBER -- when all you have is a table of values, do the best you can to ESTIMATE the tangent…

A: Given:  Aim:  Basic information:  Using central difference metthodf'xn = fxn+1-fxn-12xn-xn-1

Q: Assume that lim an = A, lim b, B. Show that n 00

A: Given that limn→∞an=A andlimn→∞bn=Bto showlimn→∞ max{an,bn}=max{A, B}

Q: Fill in the blank so that the following equation is true: æ dzdyda = 4

A:

Q: Horatio mixed blue paint and yellow paint to make green paint in the ratios given in the table…

A: You can assume the cups of blue paint and yellow paint as the coordinate(x,y) and find the equation…

Q: Find all solutions of the equation: sin(x) = 0.4 x = 1.459 + kл, where k is any integer X = = 0.412…

A:

Q: How do you solve this?

A: Given function is y=h(t)

Q: Solve the initial value problem (x² + 4)- dy + 3xy = x, y(0) = 1. dx

A: Given the differential equation,  (x2+4)dydx+ 3xy = x , y(0) = 1 (x2+4)dydx+ 3xy=x(x2+4)dydx=x -…

Q: 2) 18.49 19.9 4) 4.63 4.3 6) 10.35 10.35 8) 25.6 25.9

A: (2) 18.49 = 1849/100        19.9 = 1990/100        Since, 1849 < 1990                  =>…

Q: how do i solve this problem ? step by step please

A:

Q: How do you solve this?

A: Sum of the three angles of a triangle = pi Two of them are B=2pi/11 and C=4pi/11To find A we…

Q: During one shift, the express lane clerk recorded how many times customers violated the "10 items or…

A: To find: What is the frequency of times the limit was exceeded by more than 6 items?

Q: How do you solve this problem?

A: Note: As the question is very lengthy, we have showed the important calculations leaving the basics.…

Q: 1. Find the value of t,1 ep needed to construct a two- sided confidence interval of the given level…

A: a) From the provided information, Sample size (n) = 12 The degree of freedom = n – 1 = 12 – 1 = 11…

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.