# Verifying two functions

1. Oct 29, 2014

### terp.asessed

1. The problem statement, all variables and given/known data
I am trying to solve the textbook questions, but the steps are not shown--any suggestions would be appreciated!:

1) Verify that x(t) = Asin (wt) + B cos(wt), where w = (k/m)1/2 is a solution to Newton's equation for a harmonic oscillator.

2) Verify that x(t) = Csin(wt + Φ) is a solution to Newton's equation for a harmonic oscillator.

2. Relevant equations
Given above...

3. The attempt at a solution
1) I only have a faint idea, but don't know where to progress.....

2) I think I am going in a right direction, but don't know if it is of "ENOUGH" verification:

sin(wt +Φ) = sin(wt)cosΦ + cos(wt)sinΦ, which I put into the x(t) function:
x(t) = Csin(wt)cosΦ + Ccos(wt)sinΦ
= c1sin(wt) + c2cos(wt)

∴ c1= CcosΦ
c2= CsinΦ

...do I need further proof?

2. Oct 30, 2014

### BvU

1) The idea is that you fill in x(t) in "Newton's equation for a harmonic oscillator" . The equation is probably linear in x, so you can do the terms one by one and you can forget the constants A and B

Same goes for 2). What you do in your attempt for 2) is convert a solution of type 2) into one of type 1. So once you've done 1) properly, you are also done with 2).

You don't say, but I suppose in your context, Newton's equation for a harmonic oscillator is something like $m\ddot x + k x = 0$ ?

Last edited: Oct 31, 2014
3. Oct 30, 2014

### haruspex

... and that's the equation that should have been posted as "relevant equations".