Damped and Undamped Oscillations
Investigate Newton's Laws of motion for undamped and damped motion using pendulum systems of a tennis ball and Styrofoam ball.
* Styrofoam and tennis ball
* Pendulum apparatus
* DataStudio with motion sensor
* Graphical Analysis
For part I, a tennis ball’s dimensions were calculated then connected to a pendulum. The period of oscillation of 6 different rope lengths were graphed to determine the experimental value of gravity. Afterwards, using one common length, 5 different amplitudes were measured and the change in period was observed.
In part II, a Styrofoam ball pendulum system was used to study damped motion. The damping oscillation was obtained from a motion sensor and a DataStudio program. The period, damping constant, time constant, and quality factor were calculated both through Graphical Analysis and manually using the oscillation graph (Appendix A).
g ± Δg | 10.09 ± 0.370 m/s2 |
Graph estimate | Experimental |
ω | 4.01 rad/s | ω± Δ ω | 3.99 ± 0.011 rad/s |
τ | 58.00 s | τ± Δ τ | 57.90 ± 0.154 s |
Q | 232.48 | Q± Δ Q | 230.85 ± 0.885 |
b | 0.278 | b ± Δ b | 0.279 ± (0.982) 10-5 |
(For all the data recollected and operation see Appendix A)
Part 3- Experimental
To find decay time τ: find the intersection in on the graph in which given by the value found after:
Error propagation formulas:
ΔQ2=ω Δτ2+τ Δω2
Finding the gravitational values with error in Part I
Finding Angular Frequency for both experimental and estimated values...