6.1.5
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.
![Illustrative background for Equipment](https://image-v2.cdn.app.senecalearning.com/2018-09/5dfc4681-7924-4039-9a47-e2eca0083e24/spring-system,h_400,q_80,w_640.png)
![Illustrative background for Equipment ?? "content](https://image-v2.cdn.app.senecalearning.com/2018-09/5dfc4681-7924-4039-9a47-e2eca0083e24/spring-system,h_400,q_80,w_640.png)
Equipment
Equipment
- Suspend a mass, m, from a spring as shown in the diagram.
![Illustrative background for Method](https://image-v2.cdn.app.senecalearning.com/courseImages/physics/1.4.1 - Effects of forces/stretched-spring - Edited-min,h_400,q_80,w_640.jpg)
![Illustrative background for Method ?? "content](https://image-v2.cdn.app.senecalearning.com/courseImages/physics/1.4.1 - Effects of forces/stretched-spring - Edited-min,h_400,q_80,w_640.jpg)
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.
![Illustrative background for Method 2](https://image-v2.cdn.app.senecalearning.com/courseImages/physics/AQA New Modules/1.3.1/spring compressed,h_400,q_80,w_640.jpg)
![Illustrative background for Method 2 ?? "content](https://image-v2.cdn.app.senecalearning.com/courseImages/physics/AQA New Modules/1.3.1/spring compressed,h_400,q_80,w_640.jpg)
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.
![Illustrative background for Getting quality data](https://image-v2.cdn.app.senecalearning.com/courseImages/physics/AQA New Modules/1.1.2/string force,h_400,q_80,w_640.jpg)
![Illustrative background for Getting quality data ?? "content](https://image-v2.cdn.app.senecalearning.com/courseImages/physics/AQA New Modules/1.1.2/string force,h_400,q_80,w_640.jpg)
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.
![Illustrative background for Obtaining quality data 2](https://image-v2.cdn.app.senecalearning.com/courseImages/physics/1.3.1 - Mass,weight and density/digital-balance-min,h_400,q_80,w_640.jpg)
![Illustrative background for Obtaining quality data 2 ?? "content](https://image-v2.cdn.app.senecalearning.com/courseImages/physics/1.3.1 - Mass,weight and density/digital-balance-min,h_400,q_80,w_640.jpg)
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.
![Illustrative background for Analysis](https://image-v2.cdn.app.senecalearning.com/2018-09/74ae75a6-60e2-46d8-a9e9-5ecf5b0517ee/t2-m-graph,h_400,q_80,w_640.png)
![Illustrative background for Analysis ?? "content](https://image-v2.cdn.app.senecalearning.com/2018-09/74ae75a6-60e2-46d8-a9e9-5ecf5b0517ee/t2-m-graph,h_400,q_80,w_640.png)
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.
![Illustrative background for Equipment](https://image-v2.cdn.app.senecalearning.com/2018-09/9626b421-d0eb-42f1-872b-39cf64f4e154/pendulum-system,h_400,q_80,w_640.png)
![Illustrative background for Equipment ?? "content](https://image-v2.cdn.app.senecalearning.com/2018-09/9626b421-d0eb-42f1-872b-39cf64f4e154/pendulum-system,h_400,q_80,w_640.png)
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.
![Illustrative background for Method](https://image-v2.cdn.app.senecalearning.com/2018-03/5d4dcdba-cd42-42b4-8835-c568d153ff28/shutterstock_307728176,h_400,q_80,w_640.jpg)
![Illustrative background for Method ?? "content](https://image-v2.cdn.app.senecalearning.com/2018-03/5d4dcdba-cd42-42b4-8835-c568d153ff28/shutterstock_307728176,h_400,q_80,w_640.jpg)
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.
![Illustrative background for Obtaining quality data](https://image-v2.cdn.app.senecalearning.com/courseImages/physics/3.1.2 Internal reflection/ruler-150936_640-min,h_400,q_80,w_640.png)
![Illustrative background for Obtaining quality data ?? "content](https://image-v2.cdn.app.senecalearning.com/courseImages/physics/3.1.2 Internal reflection/ruler-150936_640-min,h_400,q_80,w_640.png)
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).
![Illustrative background for Obtaining quality data 2](https://image-v2.cdn.app.senecalearning.com/2018-03/f1ef18d7-f99d-41da-a284-646858b1c0c8/second_timer,h_400,q_80,w_640.jpg)
![Illustrative background for Obtaining quality data 2 ?? "content](https://image-v2.cdn.app.senecalearning.com/2018-03/f1ef18d7-f99d-41da-a284-646858b1c0c8/second_timer,h_400,q_80,w_640.jpg)
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.
![Illustrative background for Analysis](https://image-v2.cdn.app.senecalearning.com/2018-09/3fd234ba-8446-464b-8a61-237711642540/t2-l-graph,h_400,q_80,w_640.png)
![Illustrative background for Analysis ?? "content](https://image-v2.cdn.app.senecalearning.com/2018-09/3fd234ba-8446-464b-8a61-237711642540/t2-l-graph,h_400,q_80,w_640.png)
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.
1Measurements & Errors
2Particles & Radiation
2.1Particles
2.1.1Atomic Model
2.1.2Specific Charge, Protons & Neutron Numbers
2.1.3End of Topic Test - Atomic Model
2.1.4Isotopes
2.1.5Stable & Unstable Nuclei
2.1.6End of Topic Test - Isotopes & Nuclei
2.1.7A-A* (AO3/4) - Stable & Unstable Nuclei
2.1.8Particles, Antiparticles & Photons
2.1.9Particle Interactions
2.1.10Classification of Particles
2.1.11End of Topic Test - Particles & Interactions
2.1.12Quarks & Antiquarks
2.1.13Application of Conservation Laws
2.1.14End of Topic Test - Leptons & Quarks
2.1.15Exam-Style Question - Radioactive Decay
2.2Electromagnetic Radiation & Quantum Phenomena
3Waves
3.1Progressive & Stationary Waves
3.2Refraction, Diffraction & Interference
4Mechanics & Materials
4.1Force, Energy & Momentum
4.1.1Scalars & Vectors
4.1.2Vector Problems
4.1.3End of Topic Test - Scalars & Vectors
4.1.4Moments
4.1.5Centre of Mass
4.1.6End of Topic Test - Moments & Centre of Mass
4.1.7Motion in a Straight Line
4.1.8Graphs of Motion
4.1.9Bouncing Ball Example
4.1.10End of Topic Test - Motion in a Straight Line
4.1.11Acceleration Due to Gravity
4.1.12Projectile Motion
4.1.13Friction
4.1.14Terminal Speed
4.1.15End of Topic Test - Acceleration Due to Gravity
4.1.16Newton's Laws
4.1.17Momentum
4.1.18Momentum 2
4.1.19End of Topic Test - Newton's Laws & Momentum
4.1.20A-A* (AO3/4) - Newton's Third Law
4.1.21Work & Energy
4.1.22Power & Efficiency
4.1.23Conservation of Energy
4.1.24End of Topic Test - Work, Energy & Power
4.1.25Exam-Style Question - Forces
5Electricity
5.1Current Electricity
5.1.1Basics of Electricity
5.1.2Current-Voltage Characteristics
5.1.3End of Topic Test - Basics of Electricity
5.1.4Resistivity
5.1.5Superconductivity
5.1.6A-A* (AO3/4) - Superconductivity
5.1.7End of Topic Test - Resistivity & Superconductors
5.1.8Circuits
5.1.9Power and Conservation
5.1.10Potential Divider
5.1.11Emf & Internal Resistance
5.1.12End of Topic Test - Power & Potential
5.1.13Exam-Style Question - Resistance
6Further Mechanics & Thermal Physics (A2 only)
6.1Periodic Motion (A2 only)
6.2Thermal Physics (A2 only)
7Fields & Their Consequences (A2 only)
7.1Fields (A2 only)
7.2Gravitational Fields (A2 only)
7.3Electric Fields (A2 only)
7.4Capacitance (A2 only)
7.5Magnetic Fields (A2 only)
7.5.1Magnetic Flux Density
7.5.2End of Topic Test - Capacitance & Flux Density
7.5.3Moving Charges in a Magnetic Field
7.5.4Magnetic Flux & Flux Linkage
7.5.5Electromagnetic Induction
7.5.6Electromagnetic Induction 2
7.5.7Alternating Currents
7.5.8Operation of a Transformer
7.5.9Magnetic Flux Density
7.5.10End of Topic Test - Electromagnetic Induction
8Nuclear Physics (A2 only)
8.1Radioactivity (A2 only)
8.1.1Rutherford Scattering
8.1.2Alpha & Beta Radiation
8.1.3Gamma Radiation
8.1.4Radioactive Decay
8.1.5Half Life
8.1.6End of Topic Test - Radioactivity
8.1.7Nuclear Instability
8.1.8Nuclear Radius
8.1.9Mass & Energy
8.1.10Binding Energy
8.1.11Induced Fission
8.1.12Safety Aspects of Nuclear Reactors
8.1.13End of Topic Test - Nuclear Physics
8.1.14A-A* (AO3/4) - Nuclear Fusion
9Option: Astrophysics (A2 only)
9.1Telescopes (A2 only)
9.2Classification of Stars (A2 only)
9.3Cosmology (A2 only)
10Option: Medical Physics (A2 only)
10.1Physics of the Eye (A2 only)
10.2Physics of the Ear (A2 only)
10.3Biological Measurement (A2 only)
10.4Non-Ionising Imaging (A2 only)
10.5X-Ray Imaging (A2 only)
10.6Radionuclide Imaging & Therapy (A2 only)
11Option: Engineering Physics (A2 only)
11.1Rotational Dynamics (A2 only)
11.2Thermodynamics & Engines (A2 only)
12Option: Turning Points in Physics (A2 only)
12.1Discovery of the Electron (A2 only)
12.2Wave-Particle Duality (A2 only)
Jump to other topics
1Measurements & Errors
2Particles & Radiation
2.1Particles
2.1.1Atomic Model
2.1.2Specific Charge, Protons & Neutron Numbers
2.1.3End of Topic Test - Atomic Model
2.1.4Isotopes
2.1.5Stable & Unstable Nuclei
2.1.6End of Topic Test - Isotopes & Nuclei
2.1.7A-A* (AO3/4) - Stable & Unstable Nuclei
2.1.8Particles, Antiparticles & Photons
2.1.9Particle Interactions
2.1.10Classification of Particles
2.1.11End of Topic Test - Particles & Interactions
2.1.12Quarks & Antiquarks
2.1.13Application of Conservation Laws
2.1.14End of Topic Test - Leptons & Quarks
2.1.15Exam-Style Question - Radioactive Decay
2.2Electromagnetic Radiation & Quantum Phenomena
3Waves
3.1Progressive & Stationary Waves
3.2Refraction, Diffraction & Interference
4Mechanics & Materials
4.1Force, Energy & Momentum
4.1.1Scalars & Vectors
4.1.2Vector Problems
4.1.3End of Topic Test - Scalars & Vectors
4.1.4Moments
4.1.5Centre of Mass
4.1.6End of Topic Test - Moments & Centre of Mass
4.1.7Motion in a Straight Line
4.1.8Graphs of Motion
4.1.9Bouncing Ball Example
4.1.10End of Topic Test - Motion in a Straight Line
4.1.11Acceleration Due to Gravity
4.1.12Projectile Motion
4.1.13Friction
4.1.14Terminal Speed
4.1.15End of Topic Test - Acceleration Due to Gravity
4.1.16Newton's Laws
4.1.17Momentum
4.1.18Momentum 2
4.1.19End of Topic Test - Newton's Laws & Momentum
4.1.20A-A* (AO3/4) - Newton's Third Law
4.1.21Work & Energy
4.1.22Power & Efficiency
4.1.23Conservation of Energy
4.1.24End of Topic Test - Work, Energy & Power
4.1.25Exam-Style Question - Forces
5Electricity
5.1Current Electricity
5.1.1Basics of Electricity
5.1.2Current-Voltage Characteristics
5.1.3End of Topic Test - Basics of Electricity
5.1.4Resistivity
5.1.5Superconductivity
5.1.6A-A* (AO3/4) - Superconductivity
5.1.7End of Topic Test - Resistivity & Superconductors
5.1.8Circuits
5.1.9Power and Conservation
5.1.10Potential Divider
5.1.11Emf & Internal Resistance
5.1.12End of Topic Test - Power & Potential
5.1.13Exam-Style Question - Resistance
6Further Mechanics & Thermal Physics (A2 only)
6.1Periodic Motion (A2 only)
6.2Thermal Physics (A2 only)
7Fields & Their Consequences (A2 only)
7.1Fields (A2 only)
7.2Gravitational Fields (A2 only)
7.3Electric Fields (A2 only)
7.4Capacitance (A2 only)
7.5Magnetic Fields (A2 only)
7.5.1Magnetic Flux Density
7.5.2End of Topic Test - Capacitance & Flux Density
7.5.3Moving Charges in a Magnetic Field
7.5.4Magnetic Flux & Flux Linkage
7.5.5Electromagnetic Induction
7.5.6Electromagnetic Induction 2
7.5.7Alternating Currents
7.5.8Operation of a Transformer
7.5.9Magnetic Flux Density
7.5.10End of Topic Test - Electromagnetic Induction
8Nuclear Physics (A2 only)
8.1Radioactivity (A2 only)
8.1.1Rutherford Scattering
8.1.2Alpha & Beta Radiation
8.1.3Gamma Radiation
8.1.4Radioactive Decay
8.1.5Half Life
8.1.6End of Topic Test - Radioactivity
8.1.7Nuclear Instability
8.1.8Nuclear Radius
8.1.9Mass & Energy
8.1.10Binding Energy
8.1.11Induced Fission
8.1.12Safety Aspects of Nuclear Reactors
8.1.13End of Topic Test - Nuclear Physics
8.1.14A-A* (AO3/4) - Nuclear Fusion
9Option: Astrophysics (A2 only)
9.1Telescopes (A2 only)
9.2Classification of Stars (A2 only)
9.3Cosmology (A2 only)
10Option: Medical Physics (A2 only)
10.1Physics of the Eye (A2 only)
10.2Physics of the Ear (A2 only)
10.3Biological Measurement (A2 only)
10.4Non-Ionising Imaging (A2 only)
10.5X-Ray Imaging (A2 only)
10.6Radionuclide Imaging & Therapy (A2 only)
11Option: Engineering Physics (A2 only)
11.1Rotational Dynamics (A2 only)
11.2Thermodynamics & Engines (A2 only)
12Option: Turning Points in Physics (A2 only)
12.1Discovery of the Electron (A2 only)
12.2Wave-Particle Duality (A2 only)
![Go student ad image](/en-GB/revision-notes/_next/image?url=%2Fen-GB%2Frevision-notes%2Fimages%2Fgo-student-uk-ad.jpg&w=640&q=100)
Unlock your full potential with GoStudent tutoring
Affordable 1:1 tutoring from the comfort of your home
Tutors are matched to your specific learning needs
30+ school subjects covered