# Finding amplitude of oscillation with only k, x, v, and a

1. Jan 30, 2013

### PhizKid

1. The problem statement, all variables and given/known data
An oscillating system of a block attached to a string where k = 400 at some time t has a position x of 0.1 m, velocity of -13.6 m/s, and accel. of -123 m/s^2. Find the amplitude of the motion. Do not use energy.

2. Relevant equations
x = Acos(wt + phi)
v = -Awsin(wt + phi)
a = -Aw^2cos(wt + phi)

3. The attempt at a solution
I can solve for omega by using sqrt(-a / x), we still have 3 unknowns A, t, and phi. We have 3 equations, but they are not linear equations so I don't know how to solve them simultaneously. What other method is there that I can use since I can't use energy?

2. Jan 30, 2013

### tiny-tim

Hi PhizKid!
substitute the given values for x v and a

then you have three linear equations …

start eliminating variables

3. Jan 30, 2013

### PhizKid

But these are trig functions. Doesn't this make the equations non-linear? I'm not sure how to eliminate variables that have trig functions in them.

4. Jan 30, 2013

### tiny-tim

treat cos(wt + phi) and sin(wt + phi) as being variables in their own right!

5. Jan 30, 2013

### PhizKid

This doesn't work. When I simplify the equations for x and a, they are both identical:

alpha = cos(wt + phi)
beta = sin(wt + phi)

0.100 = A * alpha
0.100 = A * alpha
0.388 = A * beta

So it's really 2 equations with 3 unknowns... :(

6. Jan 30, 2013

### voko

There is an identity relating sin and cos. Use it.