8.1.2
Simple Harmonic Systems
SHM Experiment (Mass-Spring System)
SHM Experiment (Mass-Spring System)
A mass suspended on the end of a spring is also an excellent example of SHM.


Equipment
Equipment
- Suspend a mass, m, from a spring as shown in the diagram.


Method
Method
- The formula for the period, T, is where k is the spring constant of the spring.
- Find the length of time for 10 complete oscillations, using the pointer against the vertical scale.


Method 2
Method 2
- Repeat this and find the average time for 10 oscillations. Divide that time by 10 to find the period, T.
- The mass should be varied and the period remeasured for each value of m.
- Goggles/safety specs should be worn because there is a spring under tension.


Getting quality data
Getting quality data
- The fiducial mark should be horizontal. Some form of pointer could be attached to the suspended mass.
- You can use a small section of string between the clamp and the mass-hanger to reduce the effect of any side to side motion given to the mass in releasing it.


Obtaining quality data 2
Obtaining quality data 2
- You should check the mass, m, with a balance.
- The extension should not be so large that the elastic limit of the spring is reached. The spring should not be compressed so much that it no longer provides a restoring force.
- Keep the pointer close to but not touching the scale.
- Observe the pointer from eye level. Do this to reduce parallax errors.


Analysis
Analysis
- You should plot a graph of T² against m to verify the equation.
- You would expect to plot a straight line through the origin with a gradient .
- The straight line might miss the origin because the effective mass of the spring has not been taken into account.
- Plotted or given error bars would help to provide an estimate of the uncertainty in g by finding the worst acceptable line of fit.
SHM Experiment (Simple Pendulum System)
SHM Experiment (Simple Pendulum System)
The simple pendulum is a classic experiment to demonstrate SHM.


Equipment
Equipment
- Suspend a pendulum bob by a thread from a clamp.
- The thread should be squashed between two small blocks of wood or a bung/cork split in two. This makes the suspension point easy to define.


Method
Method
- Time for 10 oscillations. Repeat and get an average.
- Divide this average time by 10 to find the period.
- Repeat for different lengths of pendulum thread.


Obtaining quality data
Obtaining quality data
- Use a ruler to measure the length of the string from the suspension point to the centre of the bob.
- A micrometer or calipers might be useful to measure the diameter of the bob.
- Pull the bob to one side (position A) so that the thread makes a small angle with the vertical (use a protractor to measure this angle to keep it consistent and small. The maximum angle should be 10 degrees).


Obtaining quality data 2
Obtaining quality data 2
- Start and then later stop the timer when the bob passes in front of a fiducial mark placed behind the thread (i.e. position B).
- This can be a card with a vertical line drawn on, or the clamp stand.
- This mark needs to be at the equilibrium position. This is where the bob is travelling fastest, so means there is the smallest error in starting and stopping the timer.


Analysis
Analysis
- The equation for this is supposed to be . So you should plot a graph of T² against l to verify the equation.
- You would expect to see a straight line through the origin with gradient .
- You can find a value of g from the gradient ().
- Plotted or given error bars would help to provide an estimate of the uncertainty in g by finding the worst acceptable line of fit.
1Physical Quantities & Units
2Measurement Techniques
3Kinematics
4Dynamics
4.1Momentum & Newton's Laws of Motion
4.2Non-Uniform Motion
4.3Linear Momentum & Conservation
4.4Force, Density & Pressure
4.4.1Fields
4.4.2Force in Uniform Fields
4.4.3Friction
4.4.4Buoyancy
4.4.5Terminal Speed
4.4.6End of Topic Test - Acceleration Due to Gravity
4.4.7Centre of Mass
4.4.8Forces & Equilibrium
4.4.9End of Topic Test - Scalars & Vectors
4.4.10Moments
4.4.11End of Topic Test - Moments & Centre of Mass
4.4.12Density
4.4.13Pressure
4.5Work, Energy & Power
5Gravitational Fields
5.1Gravitational Fields (A2 only)
6Deformation of Solids
7Thermal Physics
7.1Thermal Physics
7.1.1Temperature
7.1.2Measuring Temperature
7.1.3Ideal Gas Law
7.1.4Ideal Gases
7.1.5Boyle's Law & Charles' Law
7.1.6Molecular Kinetic Theory Model
7.1.7Molecular Kinetic Theory Model 2
7.1.8Thermal Energy Transfer
7.1.9Thermal Energy Transfer Experiments
7.1.10End of Topic Test - Thermal Energy & Ideal Gases
7.1.11First Law of Thermodynamics
8Oscillations
8.1Simple Harmonic Motion
8.2Waves
8.2.1Progressive Waves
8.2.2Intensity of Waves
8.2.3Wave Speed & Phase Difference
8.2.4Longitudinal & Transverse Waves
8.2.5End of Topic Test - Progressive Waves
8.2.6Electromagnetic Waves
8.2.7Doppler Effect
8.2.8Sound Waves
8.2.9Measuring Sound Waves
8.2.10End of Topic Test - Waves
8.2.11Ultrasound Imaging
8.2.12Ultrasound Imaging 2
9Communication
9.1Communication Channels
9.2Digital Communication
10Electric Fields
10.1Electric Fields
11Current Electricity
11.1Current Electricity
11.1.1Basics of Electricity
11.1.2Mean Drift Velocity
11.1.3Current-Voltage Characteristics
11.1.4End of Topic Test - Basics of Electricity
11.1.5Resistivity
11.1.6End of Topic Test - Resistivity & Superconductors
11.1.7Power and Conservation
11.1.8Microphones
11.1.9Components
11.1.10Relays
11.1.11Strain Gauges
12Magnetic Fields
12.1Magnetic Fields
13Modern Physics
13.1Quantum Physics
13.1.1The Photoelectric Effect
13.1.2The Photoelectric Effect Explanation
13.1.3End of Topic Test - The Photoelectric Effect
13.1.4Collisions of Electrons with Atoms
13.1.5Energy Levels & Photon Emission
13.1.6Wave-Particle Duality
13.1.7End of Topic Test - Absorption & Emission
13.1.8Band Theory
13.1.9Diagnostic X-Rays
13.1.10X-Ray Image Processing
13.1.11Absorption of X-Rays
13.1.12CT Scanners
13.2Nuclear Physics
13.2.1Rutherford Scattering
13.2.2Atomic Model
13.2.3Isotopes
13.2.4Stable & Unstable Nuclei
13.2.5A-A* (AO3/4) - Stable & Unstable Nuclei
13.2.6Alpha & Beta Radiation
13.2.7Gamma Radiation
13.2.8Particles, Antiparticles & Photons
13.2.9Quarks & Antiquarks
13.2.10Particle Interactions
13.2.11Radioactive Decay
13.2.12Half Life
13.2.13End of Topic Test - Radioactivity
13.2.14Nuclear Instability
13.2.15Mass & Energy
13.2.16Binding Energy
13.2.17A-A* (AO3/4) - Nuclear Fusion
Jump to other topics
1Physical Quantities & Units
2Measurement Techniques
3Kinematics
4Dynamics
4.1Momentum & Newton's Laws of Motion
4.2Non-Uniform Motion
4.3Linear Momentum & Conservation
4.4Force, Density & Pressure
4.4.1Fields
4.4.2Force in Uniform Fields
4.4.3Friction
4.4.4Buoyancy
4.4.5Terminal Speed
4.4.6End of Topic Test - Acceleration Due to Gravity
4.4.7Centre of Mass
4.4.8Forces & Equilibrium
4.4.9End of Topic Test - Scalars & Vectors
4.4.10Moments
4.4.11End of Topic Test - Moments & Centre of Mass
4.4.12Density
4.4.13Pressure
4.5Work, Energy & Power
5Gravitational Fields
5.1Gravitational Fields (A2 only)
6Deformation of Solids
7Thermal Physics
7.1Thermal Physics
7.1.1Temperature
7.1.2Measuring Temperature
7.1.3Ideal Gas Law
7.1.4Ideal Gases
7.1.5Boyle's Law & Charles' Law
7.1.6Molecular Kinetic Theory Model
7.1.7Molecular Kinetic Theory Model 2
7.1.8Thermal Energy Transfer
7.1.9Thermal Energy Transfer Experiments
7.1.10End of Topic Test - Thermal Energy & Ideal Gases
7.1.11First Law of Thermodynamics
8Oscillations
8.1Simple Harmonic Motion
8.2Waves
8.2.1Progressive Waves
8.2.2Intensity of Waves
8.2.3Wave Speed & Phase Difference
8.2.4Longitudinal & Transverse Waves
8.2.5End of Topic Test - Progressive Waves
8.2.6Electromagnetic Waves
8.2.7Doppler Effect
8.2.8Sound Waves
8.2.9Measuring Sound Waves
8.2.10End of Topic Test - Waves
8.2.11Ultrasound Imaging
8.2.12Ultrasound Imaging 2
9Communication
9.1Communication Channels
9.2Digital Communication
10Electric Fields
10.1Electric Fields
11Current Electricity
11.1Current Electricity
11.1.1Basics of Electricity
11.1.2Mean Drift Velocity
11.1.3Current-Voltage Characteristics
11.1.4End of Topic Test - Basics of Electricity
11.1.5Resistivity
11.1.6End of Topic Test - Resistivity & Superconductors
11.1.7Power and Conservation
11.1.8Microphones
11.1.9Components
11.1.10Relays
11.1.11Strain Gauges
12Magnetic Fields
12.1Magnetic Fields
13Modern Physics
13.1Quantum Physics
13.1.1The Photoelectric Effect
13.1.2The Photoelectric Effect Explanation
13.1.3End of Topic Test - The Photoelectric Effect
13.1.4Collisions of Electrons with Atoms
13.1.5Energy Levels & Photon Emission
13.1.6Wave-Particle Duality
13.1.7End of Topic Test - Absorption & Emission
13.1.8Band Theory
13.1.9Diagnostic X-Rays
13.1.10X-Ray Image Processing
13.1.11Absorption of X-Rays
13.1.12CT Scanners
13.2Nuclear Physics
13.2.1Rutherford Scattering
13.2.2Atomic Model
13.2.3Isotopes
13.2.4Stable & Unstable Nuclei
13.2.5A-A* (AO3/4) - Stable & Unstable Nuclei
13.2.6Alpha & Beta Radiation
13.2.7Gamma Radiation
13.2.8Particles, Antiparticles & Photons
13.2.9Quarks & Antiquarks
13.2.10Particle Interactions
13.2.11Radioactive Decay
13.2.12Half Life
13.2.13End of Topic Test - Radioactivity
13.2.14Nuclear Instability
13.2.15Mass & Energy
13.2.16Binding Energy
13.2.17A-A* (AO3/4) - Nuclear Fusion
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