In the absence of a damping mechanism, the deplacement, go, helners cons tant k suspended oloject° and subj ected to a force of the form sinceE) by the ihihal of a spring periodic external is giren value proble m y" (t) + ky (E) =sin cet) what happens if k=4 !i!

Q: (x%ex - 2) Cln /x+il) edy xy =0 y CO) = -4 y'Co) =5 %3D

A: In this question, we find the largest interval for the solution existence of the differential…

Q: If u = x² cosy+ ye", where x = s+2t and y = st, prove that ди ди 2- (s – 21) (x siny- xye – e"). -…

A:

Q: Let C be parametrized by x = et sin (9t) and y = et cos (9t) for 0 ≤ t ≤ 2. Find the length L of C.…

A:

Q: Q4. a) Without using the shift formula prove that Laplace of f (t) = e¯“ cos wt is w? (s + a)² + w²

A: Given, ft=e-αtcoswt. To prove that, Lft=s+αs+α2+w2. By definition,…

Q: w = (x^2 + y^2)xy, x = rcosθ, y = rsinθ  a) Use chain rule to find∂w/∂r b) Find ∂w/∂rat the point…

A:

Q: 3. Consider the following helix with vector equation 7 (t) = 2 cos (t) 7 (t) 7 + tỉ + 2 sin (a)…

A:

Q: fG) = sin h e2y : find f'(y) f'G) = e2y cot hezy O None of the above. O Option 4 f'6) = e> coshe…

A:

Q: A sodium ion (Na+) moves in the xy-plane with a speed of 2.90 ✕ 103 m/s. If a constant magnetic…

A:

Q: aw Q:3) Find ду if w 2u' v+ In(5v) , u=x+y & v=e"siny

A:

Q: Compute dr where C is the ellipse 4x² + 2 = 4 (with counterclockwise 32 motion) and F(x, y) = (2++²…

A: Given Information:The vector field is given as .Ellipse equation:  with the counterclockwise…

Q: Pind the derivativa otthe Pollowing の3=2 Sin'Csx) In coshラX 3 =\nx (3) Xsin 4y=Jtan YX

A:

Q: a) z=x²ln (x y²) b) z=4 cos(x-3y)

A: Given: The functions are: (a) z=x2lnxy2 (b) z=4cosx-3y The objective is to find the second order…

Q: 10. Which one is the arc length of the given f(x)= c)1 + √2 A) 2 + √2 11. Which one is the…

A:

Q: -s Jatx? 3. 4-/ sinx coss dx |

A:

Q: Suppose that Wi is a standard Brownian motion and consider times 0 < s <t<o∞. Find E[W,W¿] and hence…

A: Given: Wt is a standard Brownian motion  0&lt;s&lt;t&lt;infinity

Q: Question 3. Find the work done by the force fie ld F = xyi+y 2j in moving a particle along the curve…

A:

Q: (a) Show that v.ve =p²o, where v- S+ denote the Laplacian operator

A: We will prove the following result.

Q: ら)1f u-L -*9 sin (2x ty), x = s? + 2t" and y= 2s -t" au using at find the chain rule Ond as

A:

Q: Consider the curve C in RS parameterized by r(t) = sin(2t) î + cos(t) ĵ+t k, con 0 <t < 2n An…

A:

Q: )y'ミ xe),Jco)=1

A: Note:  since you have posted multiple questions. As per our guidelines we are supposed to solve only…

Q: f (x) = arctan(e“) ise ƒ '(-1) =?

A: To find the derivative of  f(x)=arctan(ex) at x=-1

Q: O Let 2)=(e cut-e'snt,e'snere cost , o), te [o, ) () Find T,ĕ (umit burgent, unit binermal) () Find…

A: We have, α→t=etcost-etsint,etsint+etcost,0 we know that T→t=r→'tr→'t Now,…

Q: 22 Find the Directional Derivabive of Pary,z)= xg-y2'+Z at the point CI, -2, 0) in the direcbion of…

A:

Q: A2 pand ceghl shreldhes asprng 0.125ft. The splem, pdamped usinga dashpot with damping coefficenty=…

A:

Q: 4. Find the isolates singularities of the following functions, and determine whether they are…

A:

Q: 7 the n ya In Cx? _y?) Do not Equatio InCx-yリ Do not check modificd Laplace

A: This is a problem of partial and Laplace.

Q: Ques tion 1 : that Given 2 x?y" + x y' + 3y= 0 show 2x* ylara) lanni)x ylurs) + (2n2.n +3) ym)-

A: