Why am I getting non-sinusoidal output for sinusoidal input in mass-spring system

control theorylaplace transformsteady state

A mass spring system is represented by following transfer function

$$ H(s) = \frac{s^{2} + 0.1s + 10}{s^{4} + 0.2s^{3} + 20s^{2}} $$

but for sinusoidal input I am getting non sinusoidal output as shown below, as per my understanding response of the LTI system to sinusoidal input is sinusoidalenter image description here

I am using below MATLAB code to generate the plot

sys_x1 = tf([1,0.1,10],[1,0.2,20,0,0])    
t = 0:0.1:20;
u = sin(1*t);
lsim(sys_x1, u,t)

Best Answer

Your system is not stable -- the presence of a pole with zero real part rules out asymptotic stability; the multiplicity of the poles at zero rules out marginal stability. The statement that an LTI system generates a sinusoidal output for a sinusoidal input is only true for stable systems.

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