State the equation for the period of a simple pendulum and define every symbol.

T = 2π√(l/g), where T is the period in seconds, l the length of the pendulum from the support to the centre of the bob in metres and g the acceleration of free fall in m s⁻².

What is meant by a simple pendulum?

A simple pendulum is a small dense bob of negligible size suspended by a light inextensible thread from a fixed point, free to swing in a vertical plane.

Under what condition is the motion of a simple pendulum simple harmonic?

The angular amplitude must be small, typically less than about 10°, so that the restoring component of the weight stays very nearly proportional to the displacement.

Calculate the length of a simple pendulum whose period is 2.0 s, taking g as 9.81 m s⁻².

Rearranging gives l = gT²/(4π²) = 9.81 × 4.0/39.5 = 39.24/39.5 = 0.99 m.

CCEA A-Level Physics 1210

Physical Quantities, Scalars and Vectors

Topic overview Physical quantities and SI base units Prefixes and standard form Scalars and vectors Resolving vectors and finding resultants Coplanar forces in equilibrium

Moments and Equilibrium

Topic overview Moment of a force Centre of gravity The principle of moments Determining unknown masses using moments

Linear Motion and Dynamics

Topic overview Displacement, velocity and acceleration The equations of motion for uniform acceleration Measuring the acceleration of free fall with light gates Displacement–time and velocity–time graphs Projectile motion Projectile calculations

Newton's Laws of Motion

Topic overview Newton's first law and inertia Newton's second law and F = ma Applying Newton's laws to simple situations Newton's third law Friction as a force opposing motion

Linear Momentum and Impulse

Topic overview Momentum and its calculation Conservation of linear momentum Collisions in one dimension Elastic and inelastic collisions Impulse and the impulse–momentum equation Impacts and reducing the force of a collision Newton's second law in terms of momentum

Work, Energy and Power

Topic overview Work done and energy transfer Calculating work done, including forces at an angle Gravitational potential energy Kinetic energy Conservation of energy and energy exchanges Work done by a resultant force and change in kinetic energy Power, efficiency and energy use in society

Current, Charge and Potential Difference

Topic overview Electric current and the coulomb Potential difference and energy transfer Potential difference, power and current Electromotive force Comparing electromotive force and potential difference

Resistance and Resistivity

Topic overview Resistance and Ohm's law Ohmic and non-ohmic behaviour Resistors in series and in parallel Investigating current, voltage and resistance in series and parallel circuits Electrical power and energy in resistive circuits Resistivity and the equation R = ρl/A Measuring the resistivity of a metal Current–voltage characteristics of a conductor, a lamp and a diode Resistance, temperature and superconductivity

Internal Resistance and Potential Dividers

Topic overview Internal resistance and terminal potential difference Consequences of internal resistance for external circuits Measuring electromotive force and internal resistance The potential divider and variable output Potential dividers in lighting and heating control circuits Loaded potential dividers and output voltage calculations

Waves

Topic overview Transverse and longitudinal waves Amplitude, period, frequency and wavelength Phase and phase difference Reading wave graphs The wave equation Polarisation The electromagnetic spectrum

Refraction

Topic overview Refraction and refractive index Snell's law Measuring refractive index Total internal reflection and the critical angle Step index optical fibres The flexible endoscope

Lenses

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Superposition, Interference and Diffraction

Topic overview Superposition of waves Standing waves, nodes and antinodes Standing waves on stretched strings Standing waves in a pipe closed at one end Measuring the speed of sound with a resonance tube Conditions for observable interference Path difference and phase difference Young's double slit Diffraction at a single slit The diffraction grating

Quantum Physics

Topic overview Photons and the equation E = hf The photoelectric effect Work function, threshold frequency and Einstein's equation Energy levels in atoms Line spectra and the equation hf = ΔE Laser action X-ray production, radiography and CT scanning

Wave-Particle Duality

Topic overview Wave model, photon model and both Electron diffraction The de Broglie wavelength Calculations with the de Broglie equation

Astronomy

Topic overview The classical Doppler effect The red shift parameter z Cosmological red shift and Doppler red shift Hubble's law The age of the universe

Practical Skills and Data Analysis

Topic overview Choosing and using measuring instruments Precision, accuracy and recording measurements Using the cathode ray oscilloscope to measure voltage and frequency Tables, graphs and presenting results Linearising a relationship and using the gradient Absolute and percentage uncertainty Combining uncertainties and uncertainty on a graph Random and systematic error, reliability and refining an experiment

Deformation of Solids

Topic overview Hooke's law and the spring constant Elastic and plastic deformation and the elastic limit Stress, strain and the Young modulus Measuring the Young modulus of a wire Strain energy and force–extension graphs Choosing materials: strength, stiffness and cost

Thermal Physics

Topic overview Boyle's law, Charles's law and the pressure law The ideal gas equation pV = nRT The Avogadro constant, the mole and pV = NkT Internal energy and the distribution of molecular energy The kinetic theory equation pV = ⅓Nm⟨c²⟩Average molecular kinetic energy and temperature Absolute zero and the kelvin scale Specific heat capacity and the electrical method

Uniform Circular Motion

Topic overview Angular velocity, period and frequency Linear speed and angular velocity: v = rω Centripetal acceleration and centripetal force Applying F = mv²/r to motion at constant speed

Simple Harmonic Motion

Topic overview Defining simple harmonic motion and a = −ω²x Displacement, velocity and acceleration: x = A cos ωt The simple pendulum and T = 2π√(l/g)The loaded spiral spring and T = 2π√(m/k)SHM graphs and finding velocity from a gradient Free vibrations, forced vibrations and resonance Damping: light, critical and over-damping

The Nucleus and Radioactive Decay

Topic overview Alpha-particle scattering and the nuclear atom Nuclear radius and nucleon number The density of nuclear matter Alpha, beta and gamma radiation: nature, penetration and range Nuclear equations and changes in nucleon and proton number The random and exponential nature of radioactive decay Activity, the decay constant and A = −λN Exponential decay calculations with A = A₀e^(−λt)Half-life and measuring it

Nuclear Energy, Fission and Fusion

Topic overview Mass–energy equivalence and E = Δmc² Mass defect and binding energy The binding energy per nucleon curve Inside a fission reactor Nuclear power: social, environmental, security and economic issues The ITER tokamak fusion reactor Plasma confinement: gravitational, inertial and magnetic

Gravitational Fields

Topic overview Fields of force and field lines Gravitational field strength Newton's law of universal gravitation The field strength of a point mass Circular motion of planets and satellites Kepler's third law Geostationary satellites

Electric Fields

Topic overview Electric field strength Coulomb's law The field of a point charge Uniform fields between parallel plates Comparing gravitational and electric fields Field strength calculations and combined fields

Capacitors

Topic overview Capacitance and the farad Energy stored in a charged capacitor Capacitors in series and in parallel Charging and discharging a capacitor The exponential decay equations The time constant Flash guns and defibrillators Uses of capacitors in circuits Capacitor calculations and graph work

Magnetic Fields

Topic overview Magnetic fields around currents The force on a current-carrying conductor Magnetic flux density The electric motor Magnetic flux and flux linkage Faraday's law of electromagnetic induction Lenz's law The alternating current generator Transformers Power losses and high-voltage transmission

Charged Particles and Accelerators

Topic overview Charged particles in a uniform electric field Charged particles in a magnetic field Circular paths in a magnetic field Comparing electric and magnetic deflection The synchrotron Relativistic mass increase Antimatter and annihilation

Fundamental Particles

Topic overview Fundamental particles The four fundamental forces Classifying particles Quarks and the structure of hadrons Conservation laws Beta decay in the quark model

Simple Harmonic Motion

The simple pendulum and T = 2π√(l/g)

3 things to know
Unit A2 1

Overview

Recall questions on the period equation with every symbol, what a simple pendulum is, why the period does not depend on the mass of the bob, the small-angle condition for the motion to be simple harmonic, worked period and length calculations, and using the pendulum to determine the acceleration of free fall.

What you need to know

Answer each one before you reveal it.

Your recallNot started

Key term

Why does the period of a simple pendulum not depend on the mass of the bob?

Numbers

Calculate the period of a simple pendulum of length 0.90 m, taking g as 9.81 m s⁻².

Key term

What happens to the period of a simple pendulum if its length is quadrupled?

Questions from this subtopic

Each one with the model answer underneath.

1
State the equation for the period of a simple pendulum and define every symbol.
Model answer
T = 2π√(l/g), where T is the period in seconds, l the length of the pendulum from the support to the centre of the bob in metres and g the acceleration of free fall in m s⁻².
2
What is meant by a simple pendulum?
Model answer
A simple pendulum is a small dense bob of negligible size suspended by a light inextensible thread from a fixed point, free to swing in a vertical plane.
3
Why does the period of a simple pendulum not depend on the mass of the bob?
Model answer
The restoring force is a component of the bob's weight and is therefore proportional to its mass, and so is the inertia that opposes the acceleration, so the mass cancels out of the equation of motion.
4
Under what condition is the motion of a simple pendulum simple harmonic?
Model answer
The angular amplitude must be small, typically less than about 10°, so that the restoring component of the weight stays very nearly proportional to the displacement.
5
Calculate the period of a simple pendulum of length 0.90 m, taking g as 9.81 m s⁻².
Model answer
T = 2π√(0.90/9.81) = 2π√(0.0917) = 2π × 0.303 = 1.90 s.
6
Calculate the length of a simple pendulum whose period is 2.0 s, taking g as 9.81 m s⁻².
Model answer
Rearranging gives l = gT²/(4π²) = 9.81 × 4.0/39.5 = 39.24/39.5 = 0.99 m.

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