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A 200 g mass attached to a horizontal spring oscillates at a frequency of 2.0 Hz. At t = 0 s, the mass is at x = 5.0 cm and has vx = -30 cm/s. Determine

d) The phase constant,

f) The position at t = 0.4 s, and

g) Write down an equation that describes the position of the oscillating mass as a function of time ( ie. what is x(t)? ).

I am having difficulty doing these problems. I have no idea how to do them. For the phase constant do i just find the w, A and then use the formula x(t)=Acos(w(t)+ phi) in order to find the phase constant?

And for letter f) I have no clue as to where to start, do i have to do everything all over again? because i tried doing that by finding the w and amplitude but i dont know what to do after that. Any help would be greatly appreciated.

Hi Billy:

While this forum does not answer homework problems explicitly, I'll try to get you going in the right direction.

d) It looks like your sign convention on your phi is opposite of mine, but that should not be that big of a deal. You are correct, but with a an additional step. In the future, for these types of problems, if you know three of the four (time, phase, displacement or frequency) then you can get the fourth this the equation of motion. However assumes one knows the amplitude - which we don't yet. But we do have the velocity and so knowing that x(t) = A cos(wt-phi), we also know that dx/dt = v = -Aw sin(wt-phi). Now we just have an algebra problem where by we have two equations and two unknowns. This is just one way, you could also exploit the KE and PE equations, but I find that way takes longer.

f) once you have the phase and amplitude, go back to your equation of motion and just plug everything in to get your x

g) finally, to get your equation as a function of mass, you just have to remember that w = sqrt (k/m) and that the spring constant can be found from your energy equations.

I hope this gets you going in the right direction.

Take care!

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