Examples of simple harmonic motion

Class practical

A circus with many different examples of simple harmonic motion.

Apparatus and Materials

Station A: Simple Pendulum

• stands, 3
• clamps, 3
• bosses, 3
• G-clamps, 3
• pairs of 5 cm wood or metal blocks as jaws, 3
• pendulum bobs, 3, on strings with lengths in ratio 1:2:4

Station B: Torsional Pendulum

• pair of 5 cm wood or metal blocks as jaws
• stand, clamp and boss
• G-clamp
• short wooden rod
• wire, Eureka, effective length 50 cm, 26 SWG

Station C: Vibrating Lath

• G-clamp
• metre rule
• boss

Station D: Oscillating water column

• U-tube of water 2.5 m, filled halfway up
• disposable mouthpieces, to protect hygiene or use a simple puffer bottle to start the oscillations

Station E: Rolling ball

• steel ball or marble
• bowl, shallow and spherical

Station F: Wig-wag

• wig-wag, with 3 removable masses
• G-clamps, 2

Station G

• curtain rail, 60 cm length, 3 (circular shape, parabolic shape & V-shape) mounted on an appropriate board
• safety screen holders, 2
• steel ball or marble

Station H: Undamped light beam galvanometer

• light beam galvanometer
• cell holder with one cell
• switch
• resistance substitution box
• leads

Health & Safety and Technical Notes

Read our standard health & safety guidance

At station B, the rod used for the torsional pendulum must be balanced. Two rods fastened together with elastic bands or a shorter length of wire may also be tried.

At station C, provide a second boss-head so that students can investigate the effect of increasing the load. The position of the boss head along the length of the metre rule could also be varied.

At station D, have students alter the water levels by blowing into the tube or use a simple puffer bottle. The water will then perform damped harmonic motion. Obtaining a time trace is not easy, since the period is short and damping is high. One possibility would be using a light beam and a scalar timer, with repeated timings.

At station G , set up the board leaning backwards a little, at about 10° to 15°.

At station H, set up the circuit with the galvanometer on its least sensitive scale; then increase the sensitivity until, with a resistance of over 500 kΩ, the spot reaches almost a full-scale deflection with the switch closed. Then, with the galvanometer on its direct setting, open the switch: the spot will oscillate about its central zero position.

Procedure

At each station, displace the system from its equilibrium position and carefully observe what happens. Listen to the differences if a sound is made.

Teaching Notes

These experiments can give students a qualitative appreciation of a range of oscillators. Encourage them to use their own initiative to develop a description (graphical or otherwise) of the motion of an oscillator in its cycle. Careful work will provide the basis for discussions about the displacement, velocity and acceleration of the oscillator. You could introduce the terms displacement, amplitude, period, frequency.

Features common to all harmonic oscillations are:

• each complete oscillation of a system takes the same time
• a force returns the system to its equilibrium position when displaced
• an inertia factor makes the system overshoot its equilibrium position when in motion.

If the acceleration of a body is directly proportional to its distance from a fixed point, and is always directed towards that point, the motion is simple harmonic.

Some systems have a period of oscillation which depends on the mass. In many systems, the amplitude of oscillation decreases with time.

The link from acceleration of an oscillator to the force on the oscillator is obvious but should nonetheless be stressed as later modelling depends upon consideration of the changes in the force on an oscillator during its cycle.

Expected results for some of the stations:

• A: The periodic time, T , depends on the length, l . (The motion is isochronous.) T ∝ l^½.
• C: This behaves like a very large ticker-timer blade.
• D: The motion is damped by fluid friction but is clearly isochronous. Ask students whether period be the same if a denser liquid is used. The force tending to return the liquid to its equilibrium position will be rg D hA, where r is the fluid density, g is gravitational field strength, D h is the difference in liquid column heights, and A is the column cross-section.
• E: Listen to the sound: what does this tell you about the motion? The amplitude decreases but the frequency remains unaltered.
• F: Load the end of the wig-wag with a variable number of masses so that it oscillates sideways. Note the affect of mass on the time for one oscillation.
• G: Listen to the sound the ball makes as it rolls or slides along the tracks. The circular track will give what sounds like an isochronous motion; the parabolic track gives a frequency that increases as the amplitude decreases; the V-shaped track is not isochronous at all.
• H: A time trace for one oscillation can be obtained by photography, using a multi-slit stroboscope. Students could also record how the amplitude dies away, and isochronous property of the oscillations.