Simple harmonic motion/static equilibrium -spring problem, mass given

[mariegrdnr]

Homework Statement

A 0.500 kg mass is suspended from a spring and set into
oscillatory motion. A motion detector is used to record the motion, and it is found that its velocity function is given by V_x(t) What are:
a. the period of the motion;
b. the amplitude;
c. the maximum acceleration of the mass; and
d. the force constant of the spring?

Homework Equations

given
V_x(t)=-ωAsin(ωt+\phi)
not given but seems like the way I need to head
F_spring=-k\Deltay
T=2pi\sqrt{m/k}

The Attempt at a Solution

Did FBD where F_spring=-k\Deltay is straight up and weight=4.9N goes straight down. Giving Fnet_y=
K\DeltaL-mg=0
K\DeltaL=mg? can I make this assumption or am I missing something?
Also I have three unknowns k,\DeltaL, T and can't find another equation to substitute into for third variable. I just need to know if I am heading in the right direction for this problem.

 

[rl.bhat]

To solve the problem, one more data is essential.

 

[mariegrdnr]

Yes I agree, but none was given, so I was hoping that someone might see something:-(
Thank you for taking a look!

 

[rude man]

No, I believe it can be solved with the given info, provided that the mass was set in motion in the usual way by imparting an initial displacement to the system at rest.

Hint: determine x(t) and dx/dt as functions of time. Determine maximum dx/dt. Then determine time t1 at which dx/dt is half of max. This I believe allows solving for every parameter.