Answer:
0, 4, -4 and they may want you to mention formally all the kt multiples of
.
Step-by-step explanation:
Let's do the second derivative of the function: ![y(t)=sin(k\,t)](https://tex.z-dn.net/?f=y%28t%29%3Dsin%28k%5C%2Ct%29)
![y'(t) =k\,cos(k\,t)\\y"(t)=-k^2\,sin(kt)](https://tex.z-dn.net/?f=y%27%28t%29%20%3Dk%5C%2Ccos%28k%5C%2Ct%29%5C%5Cy%22%28t%29%3D-k%5E2%5C%2Csin%28kt%29)
So now we want:
![y"+16\,y'=0\\-k^2\,sin(kt)+\,16\,sin(kt)=0\\sin(kt)\,(16-k^2)=0\\](https://tex.z-dn.net/?f=y%22%2B16%5C%2Cy%27%3D0%5C%5C-k%5E2%5C%2Csin%28kt%29%2B%5C%2C16%5C%2Csin%28kt%29%3D0%5C%5Csin%28kt%29%5C%2C%2816-k%5E2%29%3D0%5C%5C)
Then we have to include the zeros of the binomial (
) which as you say are +4 and -4, and also the zeros of
, which include all those values of
![kt=0\,,\,\pi\,\,,\,2\pi\, ,\,etc.](https://tex.z-dn.net/?f=kt%3D0%5C%2C%2C%5C%2C%5Cpi%5C%2C%5C%2C%2C%5C%2C2%5Cpi%5C%2C%20%2C%5C%2Cetc.)
So an extra one that they may want you to include is k = 0
Answer:
y>10
Step-by-step explanation:
Let me know if this helps