dx +2 + x = F(t), dt A (non-dimensional) driven-damped harmonic oscillator model results in the following ordinary dif- ferential equation for the amplitude function x(t): d²x dt² where F(t) represents the action of the driving force. **** (ii) Solve (x) in Fourier space in terms of (w). (iii) Write the solution for x(t) in physical space as a convolution. 810 60000 (i) Take the Fourier transform of (x) to show what is the relation between (w) and (w), being them the Fourier transforms of x(t) and F(t), respectively. (iv) Find the solution ä(t) for t > 1 assuming that F(t) = { 0: 5 : 0

& Calc I (MATH-1600-WB01, MATH-1600-HSW1A) K Find the first and second derivatives. 6 dx y = 5x-5 d²y 3 || < Questio

f(x) = -2(sin(3x + pi/2)) + 1 for x is an element of [0, 4pi/3] State the phase shift, period, amplitude, zeros, range, and domain of f(x).

Write a matlab program plotting a graph with the two equations below: a(y) = (y + pi)sin(y^2 + 0.5) z(y) = (sin(2piy)cos(2piy)/exp(y - 1)) - (5/2)