Lab 11. “Simple Harmonic Motion: Mass on a Spring.”
Name: Date :
Lots of physical phenomena are caused by oscillations or vibrations. These motions could be very complex and difficult to model mathematically, however in some cases, when restoring forces are present the oscillation are simple harmonic oscillations like in the case of a mass on a spring. When a mass is hanged form a vertical spring comes to rest, any applied force in the vertical direction causes a displacement from the equilibrium position, subsequently the mass will perform simple harmonic motion.
LaB 11
objectives:
Determine the spring constant using Hooke’s Law
Determine the spring constant using the period of oscillation.
Measure the position and velocity as a function of time for an oscillating mass and spring system.
Determine the mathematical model of simple harmonic motion.
Determine the amplitude, period, and phase constant of the observed simple harmonic motion.
MATERIALS:
Mass Set
Meter Stick
Ring Stand
Spring holder
Motion Sensor
Lab Pro
Spring
Computer with Logger Pro
PRELIMINARY QUESTIONS:
Hang a mass from the spring and let a come to rest, what is true about the mass at this moment? Include a free body diagram of the situation.
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For the following situations representing the mass moving between the maximum and minimum vertical displacements, create a qualitative force diagram.
THEORY.
Hooke’s Law.
Elastic force Fk=-KX (1)
K is the elasticity constant of the spring, and x is the displacement of the equilibrium position.
The oscillation of the spring will have some period T.
(2)
We will apply the linearization process to the equation (2) , then :
(3)
PROCEDURE:
Part A: Hooke’s Law.
Measure the length of the spring (L0) and record it on the table I;
Place the spring holder on the ring stand and hang your spring from it. Please record your real spring constant, it will be provided by the professor.
Hang 100g mass from the spring, allow it to rest at the equilibrium position. Measure the new length of the spring (Ls);
Repeat steps 2 through 4 for 5 other masses;
PART B: Oscillations.
1. Connect the Motion Detector to the DIG/SONIC 1 channel of the interface;
2. Place the Motion Detector at least 40 cm below the mass. Please secure a mass so it does not fall from the spring when oscillating;
3. Open Logger Pro and make a preliminary run to make sure that the detectors “see” the mass;
4. Set the mass to oscillate, it should oscillate along a vertical line only. Click to begin data collection;
5. Record the period T, measured with the sensor, the which will provide you on the data table 2.
11. Repeat Steps 1 – 10 with different five other masses.
DATA:
Length of the Spring: L0 = .138m Real Constant: 10.0 N/m
Table I: Hooke’s Law.
Trials
1
2
3
4
5
6
Mass
m(kg)
.100
.150
.200
.250
.300
.350
Force on the Spring
Fs(N)
Length
L(m)
.210
.255
.310
.360
.407
.457
Increase in Length
ΔL (m)
Table II: Oscillation
Trials
1
2
3
4
5
6
Mass m(kg)
0.100
0.150
0.200
0.250
0.300
0.350
T(s)
0.616
0.778
0.875
1.023
1.113
1.185
ANALYSIS:
Part I: Hooke’s Law:
Determine the spring’s increase in length caused by the mass (ΔL);
Calculate the force exerted by the spring on the mass (Fs), you will need to use the equilibrium principle;
Using Logger Pro, or excel create a graph of Force on the spring vs. change in length;
Determine the spring constant using the equation of the best fit line;
What is your percentage of error?
Part II: Oscillation.
Determine the period of each oscillation;
Graph the squared period against mass. ()
Identify the slope of the graph. Calculate the elasticity constant K experimental.
Determine your percentage error.
In your lab report, write the goal, represent a free body diagram for data table, show your formulas, calculations and units. Represent two graphs, identify the slope and calculate the percent error in both cases, and write your conclusions.