There are ways to derive an accurate x0 more systematically, e.g.,
rng('default')
t = 0:0.02:10; x = t.*sin(2*pi*1*t) + 0.1*randn(1, length(t)); % x*sin(x) with noise
x = x'; t = t';
%Coarse fit
a0=mean(x);
I=t>=1;
z=(x(I)-a0)./t(I); %Ideally, z would be purely sinusoidal
cfit=fit(t(I),z,'fourier1');
% Fine fit
x0 = [a0 cfit.w/2/pi];
fitfun = fittype( @(a,b,x) a+x.*sin(2*pi*b*x) );
[cfit,gof] = fit(t,x,fitfun,'StartPoint',x0),
plot(cfit,t,x)
