Energy and Motion in a Pendulum: Introductory Physics Pendulum Lab

Energy and Motion in a Pendulum: Introductory Physics Pendulum Lab

Objective

Measure and analyze how energy transforms between kinetic and potential forms in a simple pendulum, and verify the relationship between period and length for small-angle oscillations.

Materials

• String or light rod (50–100 cm)
• Small dense bob (metal sphere or washer)
• Clamp and stand (or fixed hook)
• Stopwatch (±0.01 s preferred)
• Meter stick or ruler (mm or cm scale)
• Protractor
• Balance (optional, for mass)
• Data sheet or notebook
• Calculator or spreadsheet

Background

A simple pendulum approximates a point mass suspended from a massless, inextensible string. For small angular displacements (θ ≲ 10°), its motion is simple harmonic with period: T = 2π sqrt(L/g) where T is period, L is pendulum length, and g is gravitational acceleration. Energy alternates between gravitational potential energy (U = mgh) at maximum displacement and kinetic energy (K = ½mv^2) at the lowest point. In the ideal (no-damping) case, mechanical energy E = K + U is conserved.

Experimental Setup

1. Attach the bob to the string and secure the other end to the clamp so the bob can swing freely without touching surrounding objects.
2. Measure L from pivot to the center of mass of the bob. Record to nearest mm.
3. Use the protractor to displace the bob by a small angle (5°–10° recommended) and release without initial push.

Procedure

1. For a chosen length L (start with ~0.50 m), displace the bob by ~5° and release.
2. Use the stopwatch to time 10 consecutive oscillations; repeat this three times. Record each time and compute the average period T = time/10.
3. Repeat step 2 for at least five different lengths (e.g., 0.30, 0.40, 0.50, 0.60, 0.70 m).
4. Optional energy observations:
   • Use a motion sensor or video analysis to estimate speed at the lowest point and compute kinetic energy.
   • Measure maximum height difference Δh between equilibrium and release positions and compute potential energy change ΔU = mgΔh.
5. Estimate uncertainties: timing resolution, length measurement, and angular approximation.

Data & Analysis

• Create a table with columns: L (m), Trial times for 10 oscillations (s), Average T (s), T^2 (s^2).
• Plot T^2 versus L. For small angles, theory predicts T^2 = (4π^2/g) L — a straight line through the origin with slope 4π^2/g.
• From linear fit slope s, compute experimental g = 4π^2/s.
• Check energy conservation qualitatively: compare ΔU at release to K at bottom. For an ideal pendulum, K_max ≈ ΔU (allowing for small losses).

Sample Calculations

• Period