Knowing the closed form solution of dx/dt = 2 sin 3t − 4x, how do I construct my Simulink?

By inputting the following code in Matlab,

​​syms x(t)

eqn = diff(x) == 2*sin(3*t) - 4*x;

S = dsolve(eqn,x(0) == 0)

The output would be,

S = (6*exp(-4*t))/25 - (2*cos(3*t + atan(4/3)))/5

I know that my Simulink should be constructed as:

However I'm struggling to find how to construct the (2*cos(3*t + atan(4/3)))/5 using the two Sine waves.

I was thinking that both of their properties would be:

But I'm currently not sure if this is correct.

Any help would be greatly appreciated thank you!

[Chunru]

Why don't you put the full function in Fcn block?

[Angelica Belo]

We were given the blocks to start with and unfortunately we need to integrate the two sine blocks for this question.

Answer 1

[Paul]

So you need to express

-cos(3*t + atan(4/3))

as the sum of two sine waves. If you're allowed to make the amplitude of one of the sine waves zero, then we know that a -cos can be expressed in terms of single sin. Here's an example that you should be able to adapt to your problem

syms a
simplify(sin(a + 3*pi/2))

ans = 

Once you relate "a" to your problem, you'll be able to implement sin(a + 3*pi/2) in one Sine block, and the other Sine block won't matter as long as its Amplitude parameter is zero.

[Angelica Belo]

Thank you so much for all your help!

I got it now :)