What is the total energy of a mass–spring oscillator at any instant?

The total energy is E = ½mv² + ½kx².

How do kinetic and potential energy vary during one oscillation?

They interchange twice per cycle, the potential energy being greatest at maximum displacement and the kinetic energy greatest at the equilibrium position.

Where in the cycle is the kinetic energy of an undamped oscillator zero?

At the extremes of the motion, where the oscillator is momentarily at rest.

A spring of stiffness 20 N m⁻¹ is stretched by 0.10 m. How much energy is stored?

E = ½kx² = 0.5 × 20 × 0.010 = 0.10 J.

OCR A-Level Physics B H557

Planning

Topic overview Choosing apparatus and techniques Identifying and controlling variables Judging whether a method will work

Implementing

Topic overview Using apparatus and techniques correctly Units for measurements Recording and presenting observations

Analysis

Topic overview Processing results and reaching conclusions Significant figures and mathematical processing Graphs, gradients and intercepts

Evaluation

Topic overview Drawing conclusions and identifying anomalies Precision, accuracy and margins of error Limitations and improvements

Practical Skills

Topic overview Investigative approaches and solving practical problems Working safely with equipment and materials Following instructions and recording observations Presenting data and using software Research, referencing and choice of instruments

Use of Apparatus and Techniques

Topic overview Analogue apparatus and interpolation Digital instruments and multimeters Timing and methods that increase accuracy Calipers and micrometers for small distances Constructing and checking DC circuits Signal generators, oscilloscopes and generating waves Light, ICT and ionising radiation

Fundamental Data Analysis

Topic overview Factors affecting accuracy and uncertainty Units, prefixes, standard form and angles The language of measurement Distributions, dot-plots and graphical displays Calculating and combining uncertainties Estimating magnitudes of everyday quantities

Imaging and Signalling

Topic overview Real images and the curvature of wave-fronts Lens power and focal length The thin lens equation and the Cartesian convention Linear magnification Measuring the power and focal length of a converging lens Images as arrays of numbers Bits, bytes and the information in an image Enhancing a digital image Wave-forms, frequency and wave speed Sampling and digitising an analogue signal Noise, resolution and digital transmission Polarisation of electromagnetic waves

Sensing

Topic overview Current and the flow of charge Potential difference, e.m.f. and energy transfer Resistance, conductance and Ohm's law Series and parallel combinations Power and energy in electric circuits Internal resistance and e.m.f.Kirchhoff's laws and conservation in circuits Resistivity and conductivity Charge carrier number density in metals, semiconductors and insulators Current-potential difference characteristics and circuit components The potential divider Sensing circuits and calibration

Mechanical Properties of Materials

Topic overview Elastic and plastic deformation and fracture Hooke's law and force-extension graphs Elastic strain energy Stress, strain and the Young modulus Measuring the Young modulus and fracture stress of a metal Describing and comparing materials Metals, ceramics and polymers Direct evidence for the size and spacing of particles

Waves and Quantum Behaviour

Topic overview Waves, phase and superposition Standing waves on strings Standing waves in air columns and the speed of sound Refraction, refractive index and Snell's law Two-slit interference Diffraction at a narrow aperture The diffraction grating Measuring the wavelength of light Photons and the quantum E = hf Evidence that photons exchange energy in quanta Quantum behaviour: phasors and probability of arrival Electron diffraction and the de Broglie wavelength

Space, Time and Motion

Topic overview Scalars, vectors and their representation Resolving and adding vectors Describing motion: displacement, velocity and acceleration Motion graphs The kinematic equations for constant acceleration Projectiles and motion in two dimensions Measuring motion in the laboratory Determining the acceleration of free fall Newton's laws of motion Terminal velocity and resistive forces Momentum and impulse Conservation of momentum and collisions Work, energy and its conservation Power and modelling motion in small time steps

Creating Models

Topic overview Capacitance and charge storage Energy stored on a capacitor Capacitor discharge and the exponential model The time constant of an RC circuit Charging a capacitor Investigating capacitor charge and discharge Radioactive decay as a random process Activity, decay constant and half-life Determining the half-life of an isotope Iterative numerical models of exponential change Exponential curves on linear and logarithmic scales Simple harmonic motion: the defining relationship Solutions and graphs of simple harmonic motion Modelling oscillations step by step Energy in simple harmonic motion Period of a mass–spring system and a simple pendulum Free and forced vibrations, damping and resonance

Out Into Space

Topic overview Gravitational and kinetic energy changes Motion in a uniform gravitational field Gravitational force and the radial field Gravitational field strength Gravitational potential energy in a radial field Gravitational potential and equipotentials Graphs and diagrams of gravitational fields Angular velocity and motion in a horizontal circle Circular gravitational orbits

Our Place in the Universe

Topic overview Radar measurement of distance and velocity Distance measured in units of time Relativistic time dilation Evidence for the hot big bang Logarithmic scales of magnitude

Matter: Very Simple

Topic overview Energy transfer and specific thermal capacity Finding specific thermal capacity by an electrical method Ideal gases and the gas laws Investigating the gas laws and absolute zero Moles, the Avogadro constant and the Boltzmann constant The equation of state for an ideal gas Impulse and force–time graphs The kinetic theory of ideal gases Temperature, average energy per particle and internal energy Random walk of molecules in a gas

Matter: Hot or Cold

Topic overview Energy, temperature and the ratio E/kT The Boltzmann factor and populations of energy states Graphs of the Boltzmann factor Activation processes and the effect of temperature

Electromagnetism

Topic overview Magnetic flux, B-fields and flux linkage Electromagnetic induction: Faraday's and Lenz's laws Graphs of current, flux and induced e.m.f.The dynamo The transformer Eddy currents and real transformers Forces on current-carrying conductors Magnetic circuits, permeance and machine design Investigating induction, flux density and transformers

Charge and Field

Topic overview The uniform electric field Radial fields and the inverse square law Electric potential and potential energy Field and potential graphs Field lines and equipotential surfaces The electronvolt and accelerating charges Millikan's experiment and the discreteness of charge Moving charges in magnetic fields Comparing electric and gravitational fields

Probing Deep Into Matter

Topic overview Particle accelerators and high-energy beams Scattering and the nuclear atom Paths of scattered particles and closest approach Discrete energy levels in atoms Electron standing waves and the confined electron Quarks, hadrons and leptons Conservation laws and nuclear equations Charged particles in detectors and magnetic fields Relativistic energy and the relativistic factor

Ionising Radiation and Risk

Topic overview The nature of ionising radiations Effects on living tissue and radiation safety Absorbed dose, effective dose and risk Binding energy and nuclear stability The Nuclear Valley and modes of decay Fission, fusion and nuclear power Activity, half-life and the decay constant Investigating absorption and half-life

Creating Models

Energy in simple harmonic motion

2 things to know
Components 01, 02 and 03

Overview

Recall questions on energy stored ½kx² and Hooke's law F = kx, total energy ½mv² + ½kx², how kinetic and potential energy interchange, where kinetic energy is zero or greatest, calculating stored and total energy, maximum speed and kinetic energy at a displacement, energy in proportion to amplitude squared, and energy–displacement and energy–time graphs.

What you need to know

Answer each one before you reveal it.

Your recallNot started

Key term

What is the expression for the energy stored in a spring obeying Hooke's law?

Key term

State Hooke's law in the form used for an oscillating spring.

Questions from this subtopic

Each one with the model answer underneath.

1
What is the expression for the energy stored in a spring obeying Hooke's law?
Model answer
The stored energy is E = ½kx², where x is the extension or compression.
2
State Hooke's law in the form used for an oscillating spring.
Model answer
The force is F = kx, where k is the stiffness and x the extension or compression.
3
What is the total energy of a mass–spring oscillator at any instant?
Model answer
The total energy is E = ½mv² + ½kx².
4
How do kinetic and potential energy vary during one oscillation?
Model answer
They interchange twice per cycle, the potential energy being greatest at maximum displacement and the kinetic energy greatest at the equilibrium position.
5
Where in the cycle is the kinetic energy of an undamped oscillator zero?
Model answer
At the extremes of the motion, where the oscillator is momentarily at rest.
6
A spring of stiffness 20 N m⁻¹ is stretched by 0.10 m. How much energy is stored?
Model answer
E = ½kx² = 0.5 × 20 × 0.010 = 0.10 J.

See the rest and revise

Other ways to work this

The same content, four other ways.

What is inside Levo

Six ways to work the same material.

1Closed book

2Open book

3Closed book

The 3-step method, run for you

Answer cold, learn it, then prove it stuck. Levo tracks the jump between your first attempt and your last.

Planning

Implementing

Analysis

Evaluation

Cram a whole paper in one sitting

Sort every topic into what you know and what you do not, then drill only the weak ones.

The two charges .

attractrepelcombine

Blank Blitz makes facts automatic

Rapid timed gap-fills on the terms and numbers you need to recall without thinking.

AThe neutron has lepton number 0.

BOn the other side the proton has 0.

CThe electron has +1 and the antineutrino has −1.

Build It gets the exam shape right

Assemble a full-mark answer from its marking points, in the order an examiner wants them.

There are 2π rad in a full circle.

TrueFalse

Test It catches misconceptions

Spot the fault in a statement. The traps are the mistakes students actually make.

721941163128510

Brain Breaks between sessions

Short focus games to reset attention, so the next set lands better than the last.

Every question in Creating Models, on a schedule.

Attempt a question from memory, write the correct version, then attempt it again. Levo records the jump between your first attempt and your last, and brings each question back on the day you are due to forget it.

Start revising, £5 a month See how the method works

Or £46 a year, about £3.83 a month. Cancel anytime.