(t) = A cos(wt) + B sin(wt)? b) An undamped oscillation under the influence of external force is given by UTM& UTM s U where r(t) is the displacement at time t. Suppose a spring has mass m m- + kr = , 6 UTM and spring constant k and let w UTOs UTM U UTM F(t) = Fo cos (wot), where wo # w. What type of value k and m UTM so that the corresponding homogeneous solution is with external force m 6UTM In(t) = A cos(wt) +B sin(wt)? Hence, by using the method of undetermined coefficients, show that 5 UTM UTM SUTM UTM UTM x(t) = A cos(wt) + B sin(wt) + Fo SUTM 5UTM m(w² – w3) cos (wit). -

Q: Give the number of oscillations occurring per second for a spring-mass system that obeys the simple…

A:

Q: dz Use an appropriate form of the chain rule to find dt 1 z = 2 cos x – sin xy; x = y = 8t t' Enter…

A:

Q: dx/dt + 4x = cos(2t), x(0) = -1 Find x(t)

A:

Q: dy at t= T is dx If x=t+sin 2t , y = 3t – cos 2t, then O a. -1 O b. 1 O C. -2 O d. 2

A:

Q: dz Use an appropriate form of the chain rule to find dt 1 z = 4 cos x – sin xy; y = 7t || Enter the…

A: We have to find

Q: The acceleration of a particle moving back and forth on a lineis a = d2s/dt2 = π2 cos pt m/sec2 for…

A:

Q: Find dw/ dt at t = 0 if w = sin (xy + p), x = et, and y = ln (t + 1).

A:

Q: dw 3) Find dt if w 5 cos(xy) – sin(xy), x =,y = t, z = t3 at at 4) Let t =,u = x² - y? ,v = 4xy³.…

A:

Q: Let w = x2e2y cos 3z. Find the value of dw/ dt at the point (1, ln 2, 0) on the curve x = cos t, y =…

A: Given: w=x2e2ycos3z x=cost y=lnt+2 Putting x, y and z in w, we get…

Q: Let w = x^2e^2y cos 3z. Find the value of dw/ dt at the point (1, ln 2, 0) on the curve x = cos t, y…

A: Given  By chain rule of differentiation , we have

Q: Let y = tan(4x + 4). Find the differential dy when z 1 and da 0.4 1.631 Find the differential dy…

A: First, let us evaluate the derivative of the given function using the chain rule:…

Q: Find the total differential. w = e²y cos(7x) + z³ dw = (No Response)

A:

Q: dw Use an appropriate form of the chain rule to find dt 1 y = t, z = to w = 3 cos xy – sin xz3; t'…

A:

Q: The displacement of a structure is defined by the following equation for a damped oscillation: y=9e…

A: The displacement of a structure is defined by the equation  y=9e-0.7tcos4t…

Q: x2 dy Find - for y = x dx -for y =x cos t?dt. sť dt. 2

A:

Q: A spring attached to the ceiling is stretched 1,225 meters by a one kilogram mass. If the mass is…

A: The differential equation for the position x of the mass m of the spring mass system with mass m,…

Q: dz at t = dt if z = f(x, y) = x² – 3xy+ 2y², x = x(t) = 3 sin 2t, y = y(t) = 4 cos 2t. Use chain…

A:

Q: dz Use an appropriate form of the chain rule to find dt 1 z = 4 cos x – sin xy; x y = 7t t' Enter…

A:

Q: (a) Compute the average temperature of a wire in the shape of a helix c(t) = (cos(t), to, sin(t)), t…

A: To find- Compute the average temperature of the wire in the shape of a helix ct = cost, t10, sint, t…

Q: dz Use an appropriate form of the chain rule to find dt 1 z = 4 cos x – sin xy; x = y = 7t t' Enter…

A:

Q: dz Use an appropriate form of the chain rule to find dt 1 z = 9 cos x – sin xy; x : y = 4t t' Enter…

A:

Q: let y(t) be a solution of (cos y + 1). dy = 2t such that y(2) = 0. dt Show that sin y + y = t2 + C.…

A:

Q: dz Use an appropriate form of the chain rule to find dt z = 7 cos x – sin xy; x = ;, 1 y = 9t Enter…

A:

Q: Suppose that the position of a body moving along a coordinate line at time t is a. s = a cos kt + b…

A: Part (a):Part (a):Given,Given,

Q: dz Use an appropriate form of the chain rule to find dt 1 z = 9 cos x – sin xy; x y = 2t t' Enter…

A: This question is based on Derivative.

Q: The acceleration of a particle moving back and forth on a line is a = d2s/dt2 = pai ^2 cos pai t…

A: Given information:

Q: Find dw/ dt at t = 1 if w = xey + y sin z - cos z, x = 2sqrt(t), y = t - 1 + ln t, and z = pt.

A:

Q: B- The velocity of a particle v (msec-¹) at time t(sec) satisfies the differential dv equation…

A: We have given differential equation  tdvdt=v+t dvdt=vt+tt dvdt-vt=1 Comparing this with differential…

Q: Consider a driven oscialting spring-mass system modeled by my'' + by' + ky = Fo cos(wt). Find the…

A: Given: m=5kg K=10 N/M C=5Nsm Natural frequency ωn=km=105=2=1.4142 Critical damping coefficient…

Q: Given a particle is moving in a curve r(t) = cos 7t i + sin 7t j + 6t k. Find the tangential…

A: Given a particle is moving in a curve rt=cos 7t i^+sin 7t j^+6t k^to find the tangential and normal…

Q: dz Use an appropriate form of the chain rule to find dt z = 7 cos x – sin xy; 1 y = 7t Enter the…

A:

Q: A uniform electric field of magnitude 400 N/C is directed parallel to and in the direction of the…

A: Given: Electric field of magnitude = 400 N/C Now, Electric field equals to the gradient:

Q: dw where w = cos 8x sin 4y, x = dt and y =t". 4 Use the Chain Rule to find

A:

Q: (a) Find the differential dy. V3 + x2 dy = (22+3)() (b) Evaluate dy for the given values of x and…

A: Given query is find the differential of y and its value.

Q: If f(1, y) = 17e cos z+ 9 cot y, then the total differential of f at (0,) is O df = -17 dr + 18 dy O…

A: Given that:-     fx,y=17e-xcosx+9coty  we know that total differential is =     df=fxdx+fydy…

Q: 1- f(-vt) ve x 1tve 117e x 1, wave which is mot a solilio to wave epuation. sinncost y at3 =…

A: We need to find the solution for equation y(x)=f(ax+bt)

Q: dz Use an appropriate form of the chain rule to find dt 1 8 cos x sin ry; y = 9t t' Enter the answer…

A:

Q: Given a particle is moving in a curve r(t) = cos  7t i + sin 7t j +  8t k. Find the tangential…

A: Given a particle is moving in a curve, r(t) = cos  7t i + sin 7t j +  8t k. To Find the tangential…

Q: Find the general Solutton of differential CGu aton , 3 t.

A:

Q: dz Use an appropriate form of the chain rule to find dt 1 z = 6 cos x – sin xy; Y = 8t %3D t' Enter…

A:

Q: If f(x, y) = 16e * cos x + 4 cot y, then the total differential of f at (0, is: O df = 16 dæ – 8 dy…

A:

Q: dw 3) Find ifw = 5 cos(xy) – sin(xy),x = ,y = t,z = t³ - %3D dt

A: Given: w=5cosxy-sinxy, x=1t, y=t, z=t3 For finding dwdt, first we find w in terms of t So, we put…

Q: If f(x, y) = 22e¯ª cos x + 4 cot y, then the (0, is total differential of f at - O df = 22 dæ + 8 dy…

A:

Q: Given f(x,y,z) = 7xyz where x = sin(2t), y = cos(2t) and z = -1t. Find df/dt at t = -1. %3D Give…

A:

Q: dz Use an appropriate form of the chain rule to find dt 1 z = 5 cos x – sin xy; y = 4t t' X = Enter…

A:

Q: 3. A compression rod of length l is loaded by a sinusoidal force as shown in Figure. The bending…

A: Using the method of undetermined the coefficients for particular solution for nonhomogeneous part.

Q: (a) Consider the direction field of the differential equation dy/dx = x(y – 8)2 - 4, but do not use…

A: Since you have posted multiple questions, we will solve only first question for you. To getremaining…

Q: Show that g(x) = cos 2 =x+3 ™K(x, t) g(t) dt 0 || sin x cos t, 0≤x≤t Y sin texr

A:

Q: Q: If In/x2 +y2 =sec(), use implicit differential to proof the following: - dy (²+y*). sec?. tan?…

A: lnx2+y2=secyx