For the transfer function [ frac{Theta_{o}(s)}{Theta_{i}(s)}=frac{K_{p}}{J s^{2}+K_{p}} ] solve for (theta_{o}(t)) in terms of (J, K_{p}), and

Question:

For the transfer function

\[ \frac{\Theta_{o}(s)}{\Theta_{i}(s)}=\frac{K_{p}}{J s^{2}+K_{p}} \]

solve for $\theta_{o}(t)$ in terms of $J, K_{p}$, and $\theta_{i}(t)$. How do variations in the values of parameters $J$ and $K_{p}$ affect the behavior of $\theta_{o}(t)$ ? Discuss and show if a bounded $\theta_{i}(t)$ can be selected to destabilize response $\theta_{o}(t)$.

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