How Does a Spring's Vibration Change Over Time?

[physicsss]

A spring with spring constant 230 N/m vibrates with an amplitude of 12.0 cm when 0.530 kg hangs from it.

(a) What is the equation describing this motion as a function of time? Assume the mass passes through the equilibrium point, toward positive x (upward), at t = 0.120 s.

The equation is:
http://www.webassign.net/symImages/c/b/444b09c7ddeb5c844763b063d17f67.png

(b) At what times will the spring have its maximum and minimum lengths? (Consider only the first instances after t = 0.)

(c) What is the displacement and direction at t = 0?

(d) What is the force and its direction exerted by the spring at t = 0?

(e) What is the maximum speed?

When is it first reached after t = 0?

 

[Duarh]

So? What have you tried so far?

 

[physicsss]

I was able to find both A and w, but I can't find the phase angle...and i think everything else that follows requires it.

 

[Duarh]

You have x(t)=Acos(wt+phi). Also, you know x(0.120)=0. Do you think this might be sufficient to determine phi?

 

[Duarh]

(In addition, of course, you have to note that x is increasing at 0.120 s)

 

[physicsss]

I need help solving for c. I know that minimum length equation is -12=12*cos(wt+phi) and maximum is 12=12*cos(wt+phi), and I only w and phi, how do I solve for t using algebraic operations?

 

[physicsss]

Please, anyone?

 

[HallsofIvy]

What IS c? Your original problem made no mention of "A", "w", or "C". Are you referring to phi, the phase angle still? But then you end with "how do I solve for t using algebraic operations?" Did you mean "t" instead of "c"? Which t do you want? t is a variable.

 

[physicsss]

OK, I was able to figure out parts a and c. But for b) and e) when I solved for t, it's negative. So how to I find instances after t=0?

Also, Isn't d) just F=-kx? But the force given by the book is so small compared to my answer.

 

[Doc Al]

OK, I was able to figure out parts a and c. But for b) and e) when I solved for t, it's negative. So how to I find instances after t=0?

The motion is periodic: it repeats exactly every period. (What's the period?)

Also, Isn't d) just F=-kx? But the force given by the book is so small compared to my answer.

Yes, the force obeys Hooke's law. That probably means you found the wrong displacement at t = 0.