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Topic: EXPLORING of HARMONIC OSCILLATIONS.2) Goal: 1. Studying physical pendulum undamped oscillations description method. 2. Studying moment of inertia and equivalent length of physical pendulum determination method. 3) Scheme of laboratory research facility:
4) Table of measuring instruments:
5) Equations for calculation: 1. Statistical absolute error for direct measurements of period:
where a = 0,95 confidence probability; n = 5 number of measurements; t 0,95 ; 5 = 2,77 Students coefficient. Total absolute error of period DT = where DTDEV = 0,01s absolute instrumental error of stopwatch (see Table of measuring instruments). 2. Amplitude of oscillations A= lsinα ≈ lα here l length of a pendulum; a = 5O angle of deflection. Cyclic eigenfrequency of oscillations
where <T> average value of period of oscillations. Initial phase of oscillations: j0 =p, when initial deflection to the left and x=x(t=0)= A; j0 =0, when initial deflection to the right and x=x(t=0)= +A. Equation of oscillations of physical pendulum:
x(t)=Acos(ω0t+φ0);
where x linear displacement of pendulum; t time. 3. Experimentally determined by indirect measurement an average value of moment of inertia:
where m mass of a pendulum; g = 9.81 m/s2 acceleration due to gravity; l length of a pendulum. Absolute error for indirect measurement of moment of inertia:
where δJ relative error for indirect measurement of moment of inertia:
here 4. Theoretically determined a value of moment of inertia:
5. Average value of equivalent length of the pendulum: 6) Table of measurements m = kg; Δm =0,001 kg; l = m; Δl = 0,001 m;
7) Data processing:
8) Final results: 1. T=( <T> ± ΔT)α = (
±
)0.95 s, 2. x(t) = ×cos( t + ) m; 3. JEXP = (< J> ± ΔJ)α = (
±
)0.95 kg·m2, 4. JTHEOR = kg·m2; 5. l eq = m. 9) Conclusion: (Compare moment of inertia defined experimentally by formula (22) with that of defined by theoretical calculation by formula (23)). 10) Work done by: Work checked by:
WORK 4-3 Date: 2015-12-24; view: 925
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