Show that the displacement u(x, t) in an elastic string of length t fireed at both ends which is set in motion from its straight equilibrium position with Constant velocity vo at each point is 2} sin{ U (x, t) -sin m=1 (2n-1)² 1 (2n-1) (2n-1)пс C

Q: For an equation " + a? = 0 a) Draw a tangent vector to a solution (2(t), x'(t)) in the phase plane…

A: (a) To solve the given differential equation: Let   p=dxdt, or, x' ⇒dpdt=d2xdt2 ... differentiating…

Q: 2. a). Find the velocity and acceleration of a particle whose position function is x(t)=…

A:

Q: The motion of a mass on a spring is described by 3y" + 4y = 0, y(0) = 5, y'(0) = 6. What is the…

A: Given:The motion is described by 3y''+4y=0, y0=5, y'0=6. We have to find the amplitude of the…

Q: f(x, y) = ln(-6x – 4y), (5,6), A=6i + 8j 14 17 A) 135 135 B) C)/17 D) 11 135

A: Duf=∇f·uu

Q: For an equation x" +x = 0 a) Draw a tangent vector to a solution (x(1), x' (1)) in the phase plane…

A: (a) Solve the differential equation as follows: Let p=dxdt, or, x'. Differentiate it with respect to…

Q: Show that D^2 = {(x, y) ∈ E^2: x^2+y^2 ≤ 1} ⊂ E^2 and the space containing a single point are…

A: In algebraic topology, two topological spaces are said to be homotopy equivalent if there exists a…

Q: A particle has position function r(t) and velocity function v(t) = { 2e“, sin(−t), ln(t+1) ) (a)…

A: The given velocity function is vt=2e-t,sin-t,lnt+1

Q: Consider w = F(x,y,z) = x2 + yz3 Find the equation of the tangent when x= 3, y = 2, z = 1.  At…

A: The given surface is Fx,y,z=x2+yz3. (1) The given point is x=3,y=2, z=1. We know that the equation…

Q: z= f(x,y) ; x= r-s1 , y= r2s and zx(0,-1) = -24 ; If zx(0,-1)=-18, what is the value of the…

A: Given that z=f(x,y),     zx(0,-1)=-24 and  zy(0,-1)=-18x=r-s and y=r2s We have to find zr(0,-1).

Q: Consider a particle moving along a curve so that it is at position f(t) = (2t³, 2+²) at time t. Then…

A: Given, A particle is moving along a curve such that its position is at ft=2t3,2t2 at time t.

Q: 4. A particle moves in a straight line so that after t sec. it is S m.,from a fixed point O on the…

A: STEP 1:Given that,A particle moving in a straight line,S=t4+3t2we know that, velocity =…

Q: A spacecraft has acceleration r"(t) = , initial velocity r'(0) = and initial poition r(0) = (0, 0,…

A: GIven that a spacecraft has acceleration with initial velocity r'(0) = <2, 5, 1> and initial…

Q: Suppose F(x, y) = −y sin(x)i + cos(x)}. (a) Find a vector parametric equation for the parabola y =…

A:

Q: One model for expenditures at high school gives the cosr C, in dollars per pupil, as a function of…

A: The quadratic equation, y=ax2+bx+c can be expressed in the vertex form as y=a(x-h)2+k, where, the…

Q: Write down the equation of motion for the point particle of mass m moving in the Kepler potential…

A:

Q: 4. Compute the directional derivative of f(r, y) = at the point (1, 1) in a direction normal to the…

A:

Q: f(«, у, 2) — sec (9г + 3уг) fa = | fy = f: = ||

A:

Q: 1. A particle starts from rest and has an acceleration function, a(t) = 9-24t m/s?. a) What is the…

A: Velocity

Q: Find the general solution to the following 3-by-3 linear system: 1 -5 10 2 -4 8 X. dt 3 -5 8.

A: NOTE: According to guideline answer of first question can be given, for other please ask in a…

Q: Find the length of the curve r(t) = (ln(t))i + (2 t)j + (t²) k from t = to t = e.

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.