EXPERIMENT 1 SIMPLE HARMONIC MOTION
TOREXPERIMENT 1EPSIMPLE HARMONIC MOTIONRJohn Q. StudentSAMPLELABJanuary 1, 2013Lab Partners:Galileo GalileiIsaac NewtonMichael FaradayAlbert Einstein
DATA SHEETSIMPLE HARMONIC MOTIONJanuary 1, 2013PROCEDURE 1.3.4.Peak positions were found to be at 6.1 cm and 2.0 cm. The amplitude of themotion is therefore 6.1 – 2.0 3.1 cmAdjacent peaks were found to be at times 3.025 sec and 3.500 sec. The periodof the motion is therefore 3.500 – 3.025 0.475 sec.
PROCEDURE 2.1. Period and Amplitude.t1 (sec)t2 (sec)Period .7260.478Initial displacement (cm)c) There does not seem to be any relationship between period and amplitude. Thisindicates simple harmonic motion, since independence of the period from theamplitude is what distinguishes simple harmonic motion from other types ofharmonic motion.2. Period and Mass.Mass (g)t1 (sec)t2 (sec)Period 502.7550.60570.01.2171.8890.672c) As the mass is increased, the period of the motion increases. When the masswas doubled (from 35.0 g to 70.0 g), the period did not double; rather it increasedby a factor of 0.672/0.476 1.41 2, which suggests that the period isproportional to m.
PROCEDURE 3.1. The original equilibrium position is x 0.315 m2.Added mass Δm (g)Weight Δmg (N)New position. (m)Displacement Δx (m)Spring const. 540.00.3920.3770.0626.325. From the last column, the average value of the spring constant is found to be5.86 N/m.
ANALYSIS1. a) The period T squared as a function of mass m isT 2 4 2mkwhich is the equation of a straight line with slope 4π2/k. Using the averagemeasured spring constant k 5.86 N/m, we find a predicted slope of 4π2/(5.86 N/m) 6.74 sec2/kg.b) No, I would not expect a plot of T vs. m to show a linear relationship, since thetheoretical equation predicts T is proportional to m.c)The transformed data does show a linear plot, as predicted from the equation inpart (a) above: T2 should be proportional to m.
d) A linear regression analysis of T2 vs. m (with T in sec and m in kg) gives:Slope:5.97 sec2/kgy-intercept:0.042 sec2r:0.9605An explicit function for T2 as a function of m is thenT2 5.97 m 0.042where m is in kg and T is in seconds.e) The experimental slope (part d) and predicted slope (part a) compare fairly well,with a percent difference of (6.74-5.97)/(6.74) 100% 11%2. To double the period of the oscillator, one would need to quadruple the mass,since the period is proportional to the square root of the mass.3. To double the period of the oscillator, one would need to choose a spring whosespring constant is ¼ that of the original spring, since the period is inverselyproportional to the square root of the spring constant.
indicates simple harmonic motion, since independence of the period from the amplitude is what distinguishes simple harmonic motion from other types of harmonic motion. 2. Period and Mass. Mass (g) t1 (sec) t2 (sec) Period (sec) 35.0 1.814 2.290 0.476 45.0 3.116 3.705 0.589 55.0 2.150 2.755 0.605 70.0 1.217 1.889 0.672
Simple Harmonic Motion The motion of a vibrating mass-spring system is an example of simple harmonic motion. Simple harmonic motion describes any periodic motion that is the result of a restoring force that is proportional to displacement. Because simple harmonic motion involves a restoring force, every simple harmonic motion is a back-
Lesson 14: Simple harmonic motion, Waves (Sections 10.6-11.9) Lesson 14, page 1 Circular Motion and Simple Harmonic Motion The projection of uniform circular motion along any axis (the x-axis here) is the same as simple harmonic motion. We use our understanding of uniform circular motion to arrive at the equations of simple harmonic motion.
Simple Harmonic Motion, SHM Simple harmonic motion . Simple harmonic motion is periodic motion in the absence of friction and produced by a restoring force that is directly proportional to the displacement and oppositely directed. A restoring force, F, acts in the direction opposite the displacement of the oscillating body. F - kx. A .
Simple harmonic motion (SHM) Simple Harmonic Oscillator (SHO) When the restoring force is directly proportional to the displacement from equilibrium, the resulting motion is called simple harmonic motion (SHM). An ideal spring obeys Hooke’s law, so the restoring force is F x –kx, which results in simple harmonic motion.
SHM. Whereas, the oscillatory motion of a simple pendulum is a SHM, and since it repeats the motion in definite intervals of time called the period, T, it a periodic motion. The precise definition of a simple harmonic motion is that the net force, !⃗ on the simple harmonic oscillator has a magnitude that is
Chapter 11: Harmonic Motion 170 Learning Goals In this chapter, you will: DLearn about harmonic motion and how it is fundamental to understanding natural processes. DUse harmonic motion to keep accurate time using a pendulum. DLearn how to interpret and make graphs of harmonic motion. DConstruct simple oscillators.
SIMPLE PENDULUM AND PROPERTIES OF SIMPLE HARMONIC MOTION Purpose a. To investigate the dependence of time period of a simple pendulum on the length of the pendulum and the acceleration of gravity. b. To study properties of simple harmonic motion. Theory A simple pendulum is a small object that is suspended at the end of a string.
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