A damping force affects the vibration of a spring so that the displacement of the spring is given by y = e-4t(cos(2t) + 3 sin(2t)). Find the average value of y on the interval from t = 0 to t = π. (Round your answer to three decimal places.)

Q: Let r(t) = (sin t, 2 cos t), t = (a) Find r'(t). (b) Find T(t).

A:

Q: The figure below shows a pendulum with length L that makes a maximum angle with the vertical. +…

A:

Q: 2. Given that r(t) = 2 sin ti + 2 cos tj+ tan tk. Find the unit tangent vector T(t) at the point…

A:

Q: 1) In studying water waves, the vertical displacement y (in m) of a wave was determined to be y =…

A: Given:Vertical displacement:y=(0.5)Sin2t+(0.3)Cost   Time of interest:t = 0.40 s    ....(1) Vertical…

Q: 1. Consider the position function 7 (t) = (4 sin(2t), 2,4 cos(2t)). (a) Sketch the path of this…

A: Curvature: The curvature of postion function r→(t) is given by, κ(t) = T'(t)r'(t) Given: r→(t) =…

Q: Suppose the velocity of a particle is given by v(t) = (sin(4t), 3 cos(t), 4t³). Find the…

A: Suppose the velocity of a particle is given by v(t) = (sin(4t), 3 cos(t), 4t³). Find the…

Q: Find an equation of the tangent line to the curve at the point corresponding to the given value of…

A:

Q: T = Find the equation of the tangent line to the curve when t 6

A:

Q: Encuentre la solución general pa dy = 4 cos(e²× )sin (e²x )e²x doc Para la barra de herramientas, p

A:

Q: When starting up from rest, the angular acceleration a (in RPM/s) of a helicopter blade is a = √√8t…

A: 1. The given expression for angular acceleration is, α=8t+1​ RPM/s So, the angular velocity or the…

Q: A mass-spring system obeys simple harmonic motion according to the function f(t) = 2 cos (4). Blank…

A:

Q: = cos(8/3), 8 = π

A: The given equation is As we know