PHYSICS 151 Lab 10_ Natural Oscillations with a Spring-2-REVIEWED BY EXPERTS-GRADED A+
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Course
PHYSICS 151
Institution
University Of Hawaii, Manoa
OBJECTIVE
When a spring is stretched, and elongated it has a force applied to it. This process is on
the basis that the spring is constant. This experiment we will be using a spring to confirm
whether or not there is a way to measure the constant of a spring.
THEORY
When starting from a static...
manoaphysics 151lab 10 natural oscillations with a spring 2
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University of Hawaii, Manoa
PHYSICS 151
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OBJECTIVE
When a spring is stretched, and elongated it has a force applied to it. This process is on
the basis that the spring is constant. This experiment we will be using a spring to confirm
whether or not there is a way to measure the constant of a spring.
THEORY
When starting from a static point of view, Hooke’s law explains the stretch x of a spring
depends on the force applied F, which can be seen as the following where k is the spring constant
of s specific spring:
F = - kx
When combined with Newton’s second law of F = ma, where m is the mass attached to the
spring, and a i s the acceleration of the mass, it becomes:
ma = - kx
In this experiment acceleration a, is replaced with gravitational acceleration g giving us
x = (g / k) m
To find the spring constant, different elongations for different masses are measured. This is
described as a dynamic perspective. When the mass is attached to the spring, it will stretch and
elongate and then begin to oscillate. This results in a “simple harmonic motion.” This means that
over a certain amount of time the mass will return to the original position and velocity that it
started out with. To measure this, elongation of a spring can be shown as a function of time
where A(o) is the amplitude, and ω(o) i s the angular frequency.
x = A(o) sin( ω(o) t )
, Which is related to the period T that it takes to go through one full cycle which is
T = 1 / f = 2π / ω(o)
Velocity and acceleration of the oscillation can be calculated from the sine wave equation as a
function of time, shown as
v = ω(o) A(o) cos( ω(o) t )
and
a = -ω(o)2 A(o) sin(ω(o) t).
To achieve the relationship between the spring constant and the period, equations can be
combined to give the following:
k = ω(o)2 m = ( 4π2 / T2 ) m
This experiment works off the assumption that the mass that is attached to the spring is higher
than the mass of the spring itself.
PROCEDURE
In this experiment, different springs have different values for k. Before starting trials,
allow the spring to hang from the stand and take a measurement of the unstretched length. This is
one of the measurements needed to calculate how far the spring stretches.
FOR STATIC MEASUREMENTS
● Add weight to spring and measure how far spring is stretched
● Use masses 100 - 300 g in increments of 50 g
● Record the displacement and the corresponding mass
FOR DYNAMIC MEASUREMENTS
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