# Lab1 - Julia Bielaski 0163140 Lab Report#1 PH 327 Objective...

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Julia Bielaski 0163140 Lab Report #1 PH 327

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Objective : The purpose of this lab is to analyze oscillatory motion. The first part of the lab consists of a simple oscillator that was used to find a value for k. A mass and a spring are hung from a measured height from the ground. Additional masses are then added to the original mass and the new height is measured and recorded. The second part utilized a damped oscillator, which helped to find the frequency of oscillations by timing how long it took the mass to oscillate 30 times. The last part of the lab consisted of a driven damped oscillator. The frequency was manipulated in order to change the distance the mass oscillated inside a cylinder filled with water. Method : Simple Oscillator: F 1 is the restoring force, F 1 = - ky where k is the spring constant The natural resonance frequency f 0 =1/T where T is the period of oscillation ϖ 0 = 2 π f 0 = (k/m) Mg=k(H 0 - H) M-the added mass H 0 -the original distance between the mass and the ground H-the distance after adding a mass (H 0 - H)=(1/k)(Mg) + 0 Graphing Mg vs. (H 0 - H) will produce a slope of (1/k) Then ϖ 0 can be determined. Damped Oscillator: Damping force, F 2 = - bv b is a constant and it depends on the medium v is the velocity of oscillation (dy/dt) Part 2 of lab t 30 = for 30 oscillations f 0 = 30 / t 30 Then determine ϖ 0 using the equation ϖ 0 = 2 π f 0 Damped Driven Oscillator: Driving Force for oscillation: F 3 = F m sin( ϖ t) F m rotating vector/phasor f is the driving frequency, ϖ =2 π f Total Force=F 1 + F 2 + F 3 F=m(dv/dt)= F 1 + F 2 + F 3 v=dy/dt m(d 2 y/dt 2 )= - ky - bv+F m sin( ϖ t) Equation of Motion of a DDO Steady state solution: y(t)=y m sin( ϖ t ) φ =tan -1 [b ϖ /m( ϖ 0 2 2 )]
y m =(F m / ϖ ) / z me y m is the amplitude of oscillation z me is the mechanical impedance z me = [m 2 ( ϖ 0 2 2 ) 2 + b 2 ϖ 2 ] 1/2 / ϖ So if ϖ = ϖ 0 then z me =b and y m =F m / ϖ 0 b Data for part 1: H 0 =.98m m=.033kg g=9.8m/s 2 Table 1: Data for Part 1 M (kg) H (m) H 0 - H (m) Mg (kg*m/s 2 ) .005 .955 .025 .049 .007 .93 .05 .0686 .009 .905 .075 .0882 .011 .88 .1 .1078 .013 .86 .12 .1274 .015 .838 .142 .147 Graph 1 from part 1: A Varying Mass Hanging on a Spring y = 0.9047x 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 Mg (kg*m/s^2) slope=1/k which is .9047 according to the graph k=1.105 ϖ 0 = (k/m)= (1.105/.033) ϖ 0 =5.79 Hz

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## This note was uploaded on 04/08/2010 for the course PH PH 327 taught by Professor Roy during the Spring '10 term at Clarkson University .

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Lab1 - Julia Bielaski 0163140 Lab Report#1 PH 327 Objective...

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