I need help with finding the amplitude of this Simple Harmonic Motion problem. I think I found the frequency though.

Question

A spring with constant k = 112 N/m is sitting

vertically on the floor, and its bottom end is

attached to the floor. A 0.400-kg block is placed on

the top end of the spring and pushed downward to

start it oscillating in simple harmonic motion. The

block is not attached to the spring.

(a) Calculate the frequency f of the motion.

(b) Calculate the amplitude A that the block would

need so that the block barely begins to lose

contact with the top of the spring. (To solve

question (b), think carefully about the forces at

work on the block. As the block moves, the

forces change. First determine the location of

the block — the precise moment in its path —

at which it is most in danger of losing contact

with the spring, and draw a free-body diagram

for the block at that instant

Answer 1

So Bob L.,

The equation for the spring top is:

D(t) = - A cos (νt)

where D is position (vertical)

A is amplitude

and v is frequency

Differentiate that to find velocity, then again to find acceleration, as functions of t. You will note that there is a dependence on both v and A (to various powers!).

Losing contact means the spring acceleration at the top of the wiggle matches gravitational acceleration downwards (of the block; generally you neglect both the mass of, and the effect of gravity on, the spring itself, it doesn't deform it significantly).

Solve it from there?

-- Cheers, --Mr. d.