Undamped Spring question problem solved, but I can't plot the graph

[dwilmer]

Homework Statement

a mass weighig 2 pounds stretches a spring 6 inches. If the mass is pulled down an additional 3 inches and then released, and if there is no damping, detemine the position, u of the mass at any time, t.
Plot u verses t.
Find the frequency, period and amplitute of the motion

Homework Equations

solved all parts of the problem, but having trouble graphing the cosine wave

The Attempt at a Solution

answers: u = (1/4) cos (8t)
R = (1/4) feet
w (this is supposed to be the greek w, whatever that is called) = root k/m = 8 radians
T = 2pie/w = pie / 4

i am confused how to graph this without knowing what the phase is??
i know that amplitute will be 1/4
and the wave will have points at 0, pie/16, pie/8, 3pie/16 and pie/4
but won't i need to know phase in order to know if the waveform is shifted over at all??

..and in order to know the phase, i would need to know the coefficient in front of second term of general solution. That is:
u = (1/4)cos (8t) + B sin (8t)
and
phase = tan-1 (B/A)

therefore i have to know what B is in order to calculate phase.

Please tell me what I am doing wrong, thanks

 

[clamtrox]

You get the phase from the initial conditions. In this case you've solved it correctly, so like you said, B = 0. This is equivalent with knowing the initial position and the velocity of the mass (initial velocity = 0 <=> B = 0).

 

[HallsofIvy]

The general "wave" can be written $A cos(\omega t+ \phi)$ where A is the amplitude, $\omega$ is the frequency, and $\phi$ is the phase. In your example, the phase is 0.

(And $\omega$ is "omega", the last letter of the Greek alphabet.)