harmonic motion problem?

Question

(a) A hanging spring stretches by 35.0 cm when an object of mass 450 g is hung on it at rest. In this situation, we define its position as x = 0. The object is pulled down an additional 18 cm and released from rest to oscillate without friction. What is its position x at a time 84.4 s later?
______ cm
(b) A hanging spring stretches by 35.5 cm when an object of mass 440 g is hung on it at rest. We define this new position as x = 0. This object is also pulled down an additional 18 cm and released from rest to oscillate without friction. Find its position 84.4 s later.
______m
(c) Why are the answers to the parts (a) and (b) different by such a large percentage when the data are so simliar? Does this circumstance reveal a fundamental difficulty in calculating the future?

(d) Find the distance traveled by the vibrating object in part (a).
______m
(e) Find the distance traveled by the object in part (b).
_______ m

Answer 1

Check out:
http://en.wikipedia.org/wiki/Simple_harmonic_motion

In this case, the spring constant is defined by the initial conditions:

F = -K x D

where:
F is the force of the spring
K is the spring constant
D is the distance (change in spring length.

When a weight is suspended from the spring and all is at rest, the force the spring exerts on the weight must be equal to the force gravity exerts on the weight.

The acceleration due to gravity is approximately 9.8 m/s^2. Knowing the weights and the distances the two springs have stretched gives you the spring constants for the two springs.

The simple harmonic motion formulas from the wikipedia article give you the equations of motion, which give you the position at the specified times, as well as the distances traveled.

I'll leave part c to you.