# Second derivation function

1. Jan 15, 2010

### bokche

Can someone, please, help me solve this math problem?

z" / z = k

z=f(t)

z=?
z" - second derivative of function z=f(t)

k=const.

Thanks

2. Jan 15, 2010

### elibj123

Re write this as z''-kz=0
This is a fairly simple constant coeff. ode, solved with a characteristic polynomial.
If k>0 then you have an exponential solution (two basic solution, one tending to zero and the second grows to infinity)
If k<0 you have an oscillatory motion, with two basic solution being sine and cosine, and the angular frequency being $$\sqrt{|k|}$$

3. Jan 15, 2010

### HallsofIvy

And if k= 0, of course, the solution is linear.

(Just wanted to be complete!)

4. Jan 18, 2010

### bokche

Thanks for replies
Cheers