Hi all, I would be most grateful if I could get some help with solving the tasks below using Maple.

Given the function: mx''(t)+cx'(t)+kx(t)= F_y(t)

1. Rewrite the equation above to a system of 1. order differential equations, by defining the two variables x_1(t) = x(t) and x_2(t)=x'(t) (Hint what is x'(t)?) This gives the first differential equation in the system. What is x_2'(t)?
    
2. Write the equations as a linear system when the outer force F_y(t) is the influence and the position x_1(t) is the answer, in other words give the system matrix A and the vectors b and r.
    
3. I'm given the constants m = 5kg, c = 3Ns/m and k = 20 N/m and I'm trying to find the transfer function of the system.
    
4. Give the systems transfer function H(s) and draw the graphs for the amplitude and phase characteristic.

Thank you!

Hi, given the function f(t)=t^2. Determine the Fourier coefficients a_0, a_1 and b_1 for f(t). Plot the graphs for f(t) and also plot the graphs for the Fourier sum F(t) with N=1 in the same coordinate system. Let the t-axis go from 0 to 2*Pi.

Can someone help with this?

Thanks