# Finding the constants in a general solution

1. ### rygza

38
I have

x(t) = C(sub1) sin(16t) + C(sub2) cos(16t)

Given: initial position x(0) = 1/6
so:
1/6 = C(sub1) sin(0) + C(sub2) cos(0)
1/6 = C(sub2)

but how do i find C(sub1)? im not given initial velocity

2. ### Fragment

150
Well you have:

C1*sin(16t)+(1/6)cos(16t)=0

It's possible to isolate C1 here with simple algebra. What do you get when you try this?

3. ### SEngstrom

52
No, you don't have enough information to determine $$C_1$$.

4. ### rygza

38
C1 = (-1/6)*(cos(16t)/sin(16t))

im a allowed to do that (set the eq. to zero)?

also, the book answer is x(t) = (1/6)*cos(16t)
so C1 must be zero, but i cannot solve for C1(cant plug in initial position 0 because that would be dividing by zero.

5. ### SEngstrom

52
C1 is not a constant if it depends on 1/tan(16t).
Besides, that comes from assuming that x(t) is zero everywhere, which you did not state in the problem.

You have only presented one equation to extract information from: x(0)=1/6. It is not possible to determine both constants from one piece of information. Any value for $$C_1$$ is consistent with the information you have given us. Is there more?

6. ### rygza

38
sooo sorry. I've been reading the problem over and over (it's actually a mass on spring problem). It uses the term "from rest", meaning initial velocity is 0. Now when i solve for the constants i get

0 = 16C1 and C1 = 0

Wow, an hour wasted because i missed that part

7. ### SEngstrom

52
Good start on any problem to count the number of unknowns and see what information you need to hunt 'em down :-)

8. ### HallsofIvy

40,308
Staff Emeritus
I once watched a calculus lesson on a local educational station. The problem was the typical "a rock is dropped from height....". In the middle of the problem the instructor said "We are not told the initial speed so we will take that to be 0." I nearly threw a brick through the television screen!

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