# lab sheet

Topics: Mass, Classical mechanics, Force Pages: 2 (386 words) Published: December 5, 2013
If a weight, W = mg, is hung from one end of an ordinary spring, causing it to stretch a distance x, then an equal and opposite force, F, is created in the spring which opposes the pull of the weight. If W is not so large as to permanently distort the spring, then this force, F, will restore the spring to its original length after the load is removed. The magnitude of this restoring force is directly proportional to the stretch,

F = -kx

The constant k is called the spring constant. To emphasize that x refers to the change in length of the spring we write
F = mg = - k ∆ l (1)

In this form it is apparent that if a plot of F as a function of ∆ l has a linear portion, this provides confirmation that the spring follows Hooke's Law and enables us to find k. The constant k is called the spring constant. To emphasize that x refers to the change in length of the spring we write

F = mg = - k ∆ l (1)

In this form it is apparent that if a plot of F as a function of ∆ l has a linear portion, this provides confirmation that the spring follows Hooke's Law and enables us to find k.
An additional approach is possible. One definition of simple harmonic motion is that it is motion under a linear, “Hooke's Law” restoring force. Note that for simple harmonic motion, the period does not depend upon the amplitude of the oscillation. For such a motion, we have

2 2 T = 4π m/ k (2)
where k again is the spring constant, T is the period of the pendulum and m is the mass that is oscillating. Thus, the mass includes the mass of the spring itself. However, the entire spring does not vibrate with the same amplitude as the load (the attached mass) and therefore it is reasonable to assume that the effective load (m) is the mass hung from the end of the spring plus some fraction of the mass of the spring. Based on similar experiments, one third of the mass of the spring is a good estimation of the effective load due to the spring, thus

1
3
m m=...

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