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:

1 – physical pendulum; 2 – ruler; O – pivot point; C – center of gravity; leq – equivalent length; α – angle of deflection; a – distance between pivot point (axis of rotation) and center of gravity; – quasi-elastic force; – supporting force; –gravity force.

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 – Student’s coefficient.

Total absolute error of period

DT = ,

where DT_DEV = 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 = 5^O – 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 δ_J – relative error for indirect measurement of moment of inertia:

,

here , , – relative errors for mass, length and period of the pendulum; Δm, Δl, ΔT – absolute errors for mass, length and period of the pendulum.

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;

№	ti, s	Ti, s	ΔTi, s	(ΔTi)2, s2
1.
2.
3.
4.
5.
average value <T>=	…		…

7) Data processing:

…

8) Final results:

1. T=( <T> ± ΔT)_α = ( … ± … )_0.95 s, = … %.

2. x(t) = … ×cos(…t +…) m;

3. J_EXP = (< J> ± ΔJ)_α = ( … ± … )_0.95 kg·m², = … %;

4. J_THEOR = … 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: 769