6. Find the Laplace transform L{f} of the function f below. f(t) = 7t - sin(8t) + 3t cos(4t)
Ans =sqrt(2)cos(10^7t)cos(2.5*10^5t-pi/4) Plz show all the steps In the circuit below, assume that 1,0) = (1 mA) cos25x 105) cos(107t). Find v (t). i (t) 10 uH 1000 pF Hint: from trigonometry, cos(a + b) = cos(a) cos(b)-sin(a) sin(b) cos(a-b) = cos(a) cos(b) + sin(a) sin(b) Adding these two equations removes the sin terms, giving cos(a + b) + cos(a-b) = 2 cos(a) cos(b) Therefore, a signal that is the product of two cosine waveforms at given frequen- cies can...
Let r(t) = <cos(5t), sin(5t), v7t>. (a) (7 points) Find |r'(t)|| (b) (7 points) Find and simplify T(t), the unit tangent vector. Upload Choose a File
(1 point) Find the solution r(t) of the differential equation with the given initial condition: r' (t) = (sin 2t, sin 5t, 3t) , r(0) = (5,8,6) r(t) =(
for the curve r(t) find an equation for the indicated plane at the given value of t 56) r(t) (t2-6)i+ (2t-3)j+9k; osculating plane at t=6 A) x+ y+(z+9)=0 C)x+y+ (z-9)-0 56) B) z-9 D) z -9 (3t sint+3 cos t)i + (3t cos t-3 sin t)j+ 4k; normal plane at t 1.5r.. A) y=-3 57) r(t) 57) B) y 3 C)x-y+z-3 D) x+y+z=-3 56) r(t) (t2-6)i+ (2t-3)j+9k; osculating plane at t=6 A) x+ y+(z+9)=0 C)x+y+ (z-9)-0 56) B) z-9 D)...
(1 point) For the curve given by r(t) = (2t, 5t, 1 – 5t), Find the derivative r'(t) =( > Find the second derivative p"(t) = ( 1 Find the curvature at t = 1 K(1) =
calculus 3 8. The position of a particle moving in a circular path is given by r(t) =< -4 sin(3t), 4 cos(3t) >. Find the speed v of the particle at any time t.
Question 7 Let r(t) = ( 11t, cos 5t, sin 5t> Find the unit tangent vector and the unit normal vector of r(t) at + = (Round to 2 decimal places) TE == NG) = < bic rocnonse
(1 point) Evaluate s(t) du for the Bermoulli spiral r(t) -(e cos(5t), e sin(5t,) It is convenient to take -oo as the lower limit since s(-oo) 0. Then use s to obtain an arc length parametrization of r (t). (1 point) Evaluate s(t) du for the Bermoulli spiral r(t) -(e cos(5t), e sin(5t,) It is convenient to take -oo as the lower limit since s(-oo) 0. Then use s to obtain an arc length parametrization of r (t).
For a given law of motion of a particle M find a location of a particle for a time ty (in sec), trajectory, velocuty, tangential, normal and full acceleration -2t +3 4 cos (xt/3) 2 4 sin2(xt/3) sin(rt/3) -1 4t +4 2sin(t/3) 3e2 +2 3t2 + 7 sin(rt/6) +3 -3cos(nt/3) + 4 -141 1/2 2os(t/6) 4 cos(t/3) 10 83t 5 cos (t/6)-3 -5 sin rt2/3) 1/2 5 sin2(xt/6) 5 cos(rt2/3) -2t-2 412 13 14 4 cos(xt/3) 3sin(rt/3) 16 3t 1/2...