7.1.2

Simple Harmonic Systems

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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 T=2πmkT=2\pi \sqrt{\frac{m}{k}} 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 =4π2k=\frac{4\pi^2}{k}.
  • 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)

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 T=2πlgT = 2\pi \sqrt{\frac{l}{g}}. 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 =4π2g= \frac{4\pi^2}{g}.
  • You can find a value of g from the gradient (g=4π2gradientg = \frac{4\pi^2}{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.
Jump to other topics
1

Physical Quantities & Units

1.1

Physical Quantities & Units

1.1.1Use of SI Units1.1.2SI Prefixes, Standard Form & Converting Units1.1.3End of Topic Test - Units & Prefixes1.1.4Avogadro's Constant1.1.5Scalars & Vectors
1.2

Errors & Uncertainty

1.2.1Measuring Length, Time & Volume1.2.2Measuring Temperature1.2.3Circuit Measurements1.2.4Limitation of Physical Measurements1.2.5Uncertainty1.2.6Estimation1.2.7Displaying Data1.2.8End of Topic Test - Measurements & Errors
2

Kinematics

2.1

Equations of Motion

2.1.1Motion in a Straight Line2.1.2Graphs of Motion2.1.3Bouncing Ball Example2.1.4End of Topic Test - Motion in a Straight Line2.1.5Acceleration Due to Gravity
3

Dynamics

3.1

Momentum & Newton's Laws of Motion

3.1.1Mass & Inertia3.1.2Newton's Laws3.1.3Momentum3.1.4End of Topic Test - Newton's Laws & Momentum3.1.5A-A* (AO3/4) - Newton's Third Law
3.2

Non-Uniform Motion

3.2.1Projectile Motion
3.3

Linear Momentum & Conservation

3.3.1Conservation of Momentum
4

Force, Density & Pressure

4.1

Force, Density & Pressure

4.1.1Fields4.1.2Force in Uniform Fields4.1.3Friction4.1.4Buoyancy4.1.5Terminal Speed4.1.6End of Topic Test - Acceleration Due to Gravity4.1.7Centre of Mass4.1.8Forces & Equilibrium4.1.9End of Topic Test - Scalars & Vectors4.1.10Moments4.1.11End of Topic Test - Moments & Centre of Mass4.1.12Density4.1.13Pressure
5

Work, Energy & Power

5.1

Work, Energy & Power

5.1.1Work & Energy5.1.2Power & Efficiency5.1.3Conservation of Energy5.1.4End of Topic Test - Work, Energy & Power
5.2

Gravitational Fields

5.2.1Newton's Law5.2.2Gravitational Field Strength5.2.3Gravitational Potential
6

Deformation of Solids

6.1

Materials

6.1.1Bulk Properties of Solids6.1.2Energy in Materials6.1.3Young Modulus6.1.4End of Topic Test - Materials
7

Waves

7.1

Simple Harmonic Motion

7.1.1Simple Harmonic Motion7.1.2Simple Harmonic Systems7.1.3Energy in Simple Harmonic Motion7.1.4Resonance7.1.5End of Topic Test - Simple Harmonic Motion7.1.6A-A* (AO3/4) - Simple Harmonic Motion7.1.7End of Topic Test - Gravitational Fields
7.2

Waves

7.2.1Progressive Waves7.2.2Intensity of Waves7.2.3Wave Speed & Phase Difference7.2.4Longitudinal & Transverse Waves7.2.5End of Topic Test - Progressive Waves7.2.6Electromagnetic Waves7.2.7Doppler Effect7.2.8Sound Waves7.2.9Measuring Sound Waves7.2.10End of Topic Test - Waves7.2.11Ultrasound Imaging7.2.12Ultrasound Imaging 2
8

Superposition

8.1

Superposition

8.1.1Stationary Waves8.1.2Stationary Waves 28.1.3End of Topic Test - Stationary Waves8.1.4A-A* (AO3/4) - Stationary Waves8.1.5Interference8.1.6Interference 28.1.7End of Topic Test - Interference8.1.8Diffraction8.1.9Diffraction Gratings8.1.10End of Topic Test - Diffraction
9

Thermal Physics

9.1

Circular Motion

9.1.1Circular Motion9.1.2Circular Motion 29.1.3End of Topic Test - Circular Motion
9.2

Thermal Physics

9.2.1Temperature9.2.2Measuring Temperature9.2.3Ideal Gas Law9.2.4Ideal Gases9.2.5Boyle's Law & Charles' Law9.2.6Molecular Kinetic Theory Model9.2.7Molecular Kinetic Theory Model 29.2.8Thermal Energy Transfer9.2.9Thermal Energy Transfer Experiments9.2.10End of Topic Test - Thermal Energy & Ideal Gases9.2.11First Law of Thermodynamics
10

Communication

10.1

Communication Channels

10.1.1Communication Channels10.1.2Modulation10.1.3Attenuation
10.2

Digital Communication

10.2.1Digital & Analogue Signals10.2.2Representing Sound
11

Electric Fields

11.1

Electric Fields

11.1.1Coulomb's Law11.1.2Electric Field Strength11.1.3Electric Field Strength 211.1.4Electric Potential11.1.5End of Topic Test - Electric Fields11.1.6A-A* (AO3/4) - Electric and Gravitational Field
11.2

Capacitance

11.2.1Capacitance11.2.2Parallel Plate Capacitor11.2.3Energy Stored by a Capacitor11.2.4Capacitor Discharge11.2.5Capacitor Charge
12

Current Electricity

12.1

Current Electricity

12.1.1Basics of Electricity12.1.2Mean Drift Velocity12.1.3Current-Voltage Characteristics12.1.4End of Topic Test - Basics of Electricity12.1.5Resistivity12.1.6End of Topic Test - Resistivity & Superconductors12.1.7Power and Conservation12.1.8Microphones12.1.9Components12.1.10Relays12.1.11Strain Gauges
12.2

DC Circuits

12.2.1Circuits12.2.2Potential Divider12.2.3Emf & Internal Resistance12.2.4End of Topic Test - Power & Potential
13

Magnetic Fields

13.1

Magnetic Fields

13.1.1Magnetic Flux Density13.1.2End of Topic Test - Capacitance & Flux Density13.1.3Moving Charges in a Magnetic Field13.1.4Magnetic Flux & Flux Linkage13.1.5Electromagnetic Induction13.1.6Electromagnetic Induction 213.1.7Magnetic Flux Density13.1.8Magnetic Resonance Scanning
13.2

Alternating Currents

13.2.1Alternating Currents13.2.2Operation of a Transformer13.2.3End of Topic Test - Electromagnetic Induction & AC13.2.4Rectification
14

Modern Physics

14.1

Quantum Physics

14.1.1The Photoelectric Effect14.1.2The Photoelectric Effect Explanation14.1.3End of Topic Test - The Photoelectric Effect14.1.4Collisions of Electrons with Atoms14.1.5Energy Levels & Photon Emission14.1.6Wave-Particle Duality14.1.7End of Topic Test - Absorption & Emission14.1.8Band Theory14.1.9Diagnostic X-Rays14.1.10X-Ray Image Processing14.1.11Absorption of X-Rays14.1.12CT Scanners
14.2

Nuclear Physics

14.2.1Rutherford Scattering14.2.2Atomic Model14.2.3Isotopes14.2.4Stable & Unstable Nuclei14.2.5A-A* (AO3/4) - Stable & Unstable Nuclei14.2.6Alpha & Beta Radiation14.2.7Gamma Radiation14.2.8Particles, Antiparticles & Photons14.2.9Quarks & Antiquarks14.2.10Particle Interactions14.2.11Radioactive Decay14.2.12Half Life14.2.13End of Topic Test - Radioactivity14.2.14Nuclear Instability14.2.15Mass & Energy14.2.16Binding Energy14.2.17A-A* (AO3/4) - Nuclear Fusion

Practice questions on Simple Harmonic Systems

Can you answer these? Test yourself with free interactive practice on Seneca — used by over 10 million students.

  1. 1
    What is the correct equation for the period T of a mass-spring system?Multiple choice
  2. 2
    Finding spring constant experimentPut in order
  3. 3
    The fiducial mark for the timer should be set when the bob of the pendulum is moving fastest, where is this?Multiple choice
  4. 4
    Which statements about a pendulum SHM system are true? True / false
  5. 5
    What is the gradient of a graph of T<sup>2</sup> against l in simple harmonic motion?Multiple choice
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Simple Harmonic Motion

Energy in Simple Harmonic Motion