Experiment 18b

# Experiment 18b - 2 cos[(2π/0.94s)(0.8200s)] = -3.727 m/s 2...

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Experiment 18b – Simple Harmonic Motion: Sinusoidal Behavior in the Spring Mass System Table I shows the gate number (gate), displacement [y(cm)], time [t(s)], velocity [v(m/s)], and acceleration [a(m/s 2 )] as determined in the experiment. Table I: Experimental Data Gate y(cm) t(s) v(m/s) a(m/s 2 ) --- --- --- Expt. Theo. Expt. Theo. 1 +12 0s --- 0 --- -5.361(m/ s 2 ) 2 +9 0.8200s 0.395m/s 0.577m/s 4.046(m/s 2 ) -3.727(m/ s 2 ) 3 +6 0.598m/s 4 +3 0.6033s 0.662m/s 0.624m/s 2.722(m/s 2 ) 3.370(m/s 2 ) 5 0 0.719m/s 6 -3 0.4422s 0.666m/s -0.148m/s -1.009(m/ s 2 ) 5.269(m/s 2 ) 7 -6 0.595m/s 8 -9 0.2650s 0.452m/s -0.786m/s -3.098(m/ s 2 ) 1.068(m/s 2 ) Calculations: ω = 2π/T T = 0.94s y m = 0.12m v = dy/dt = -y m ω sin(ωt) v = -0.12m(2π/0.94s)sin[(2π/0.94s)(0s)] = 0 m/s v = -0.12m(2π/0.94s)sin[(2π/0.94s)(0.8200s)] = 0.577 m/s v = -0.12m(2π/0.94s)sin[(2π/0.94s)(0.6033s)] = 0.624 m/s v = -0.12m(2π/0.94s)sin[(2π/0.94s)(0.4422s)] = -0.148 m/s v = -0.12m(2π/0.94s)sin[(2π/0.94s)(0.2650s)] = -0.786 m/s a = d 2 y/dt 2 = -y m ω 2 cos(ωt) a= -0.12m(2π/0.94s) 2 cos[(2π/0.94s)(0s)] = -5.361 m/s 2 a= -0.12m(2π/0.94s)

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Unformatted text preview: 2 cos[(2π/0.94s)(0.8200s)] = -3.727 m/s 2 a= -0.12m(2π/0.94s) 2 cos[(2π/0.94s)(0.6033s)] = 3.370 m/s 2 a= -0.12m(2π/0.94s) 2 cos[(2π/0.94s)(0.4422s)] = 5.269 m/s 2 a= -0.12m(2π/0.94s) 2 cos[(2π/0.94s)(0.2650s)] = 1.068 m/s 2 Figure I shows the experimentally determined acceleration, displacement, and velocity as a function of time. Series 1 shows displacement, Series 2 shows velocity, and Series 3 shows acceleration (all as a function of time). Figure I Figure I-4-2 2 4 6 8 10-2 2 4 6 8 10 12 14 t(s) Series1 Series2 Series3 Table II shows the maximum values as found in the experiment and percent error. Table II Theo Expt % Err v(m/s) 0.624m/s 0.719m/s 13.2% a(m/s 2 )-3.727(m/s 2 ) 4.046(m/s 2 ) 208.5% y(cm)---12---Calculations: (Actual – Experimental)/Actual x 100 (0.719m/s – 0.624m/s)/0.719m/s x 100 = 13.2% [-3.727(m/s 2 ) - 4.046(m/s 2 )]/ -3.727(m/s 2 ) x 100 = 208.5%...
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## This note was uploaded on 04/30/2008 for the course PHY 201 taught by Professor Dr.orehotsky during the Spring '06 term at Wilkes.

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Experiment 18b - 2 cos[(2π/0.94s)(0.8200s)] = -3.727 m/s 2...

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