PHY 122 LAB : PRACTICAL ON SPRINGS AND OSCILLATORS
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Course
PHYSICS
Institution
PHYSICS
Introduction
In this lab we will measure the static behavior (stretch vs. force) of simple springs, practice linear fits to find the static spring constant, then make an oscillator and test the relationship between frequency and mass to get the dynamic spring constant. Springs, like those in your ...
Introduction
In this lab we will measure the static behavior (stretch vs. force) of simple springs,
practice linear fits to find the static spring constant, then make an oscillator and test the
relationship between frequency and mass to get the dynamic spring constant. Springs,
like those in your car's suspension, or between atoms in solids, are important because
they produce simple harmonic oscillator motion (SHM), which occurs throughout all of
physics and electrical and mechanical engineering. Text Reference: Y&F 6.3, 13.2.
Theory - Hooke's law and Simple Harmonic Motion.
An ideal spring is massless and linear. That is, it obeys Hooke’s law:
F(X)=-ks (X-X0) Eq. 1
where F is the force exerted by the spring (it opposes the stretch) and (X-X0) is the
stretch, measured from the resting position (zero force at X0), and ks is the static spring
constant. In this lab, the force arises from calibrated weights hung vertically. Hence, we
have F = mg. F is in Newtons for “m” in kg and g = 9.80 m/sec2. (Real springs have mass
and are a little non-linear. In this case, it is useful to define a local or differential spring
constant in terms of the derivative
kloc(X)= dF/dX. Eq. 2
Note that kloc then varies with stretch).
Now read the "Curve Fitting" pdf on the class web page - it is ESSENTIAL for this lab.
An object that is subject to such a linear restoring force will undergo "simple
harmonic motion" if it is displaced and let go. Our mass on a spring is a simple
common example, similar to that which occurs in your car on its springs. A
pendulum is also an oscillator, with all the same formalism, but with position
measured along the arc of motion.
We can simplify eqn 1 now if we take Xo = 0, so that
F = -kd X. Eq.3
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