Problem $3(20$ Points$)$

A dynamic system is described as

$y^{}(t)+2K{y}^{}(t)+4y(t)=u$

$y(0)=1,y^{}(0)=2$

where K is a constant.

$(1)K=1,$ find the unit impulse response.

$(2)$ Find the condition in terms of $K$ such that the system response is stable.

$(3)$ If the desired overshoot for a step input should be less than $10\%,$ can you find the range of K $?$