Harmonic motion with a spring question

[Norm850]

A 0.1-kg mass is attached to a spring having a spring constant 3.6 kg/s^2. The system is allowed to come to rest. Then the mass is given a sharp tap, imparting an instantaneous downward velocity of 0.4 m/s. If there is no damping present, find the amplitude A and frequency ω of the resulting motion.

A) Let x=0 be the position of the spring before the mass was hung from it. Find x(0).

If x(t) is the displacement, then wouldn't x(0) = 0 since this is before the mass was hung from it?

B) Solve this initial value problem and plot the solution.

Once I figure out A, I am sure I can do B.

 

[tiny-tim]

Hi Norm850!

I think they mean that x(0) is the equilibrium position after the mass is hung from it (and therefore at t = 0 when the mass is tapped).

Find x(0) by balancing the weight down against the spring force up.