كيف يحسب الرقم الهيدروجيني pH للمحاليل؟ How to calculate pH and pOH?

يحسب الرقم الهيدروجيني بالعلاقة: pH = -log[H⁺]، وللمحاليل المائية عند 25°C: pH + pOH = 14. إذا كان pH 7 فالمحلول قاعدي. [الصيغة الرمزية الموزونة: pH = -log[H⁺] | pOH = -log[OH⁻] | pH + pOH = 14 | [H⁺][OH⁻] = 10⁻¹⁴]

Theme C — Wave Behaviour

C.1 Simple Harmonic Motion — IB Physics HL Revision Notes & Topical Questions

5 min read 12 parts Lesson 2 of 37 1 quiz

📚 IB Physics HL Hub / Topical Revision

Curriculum Equation Key قوانين الرقم الهيدروجيني والاتزان الأيوني - pH & Acid-Base Equilibrium FormulasFast Exam Solution

pH = -log[H⁺]  |  pOH = -log[OH⁻]  |  pH + pOH = 14  |  [H⁺][OH⁻] = 10⁻¹⁴

Word Equation & Conditions: الرقم الهيدروجيني = -لوغاريتم تركيز أيون الهيدروجين | pH + pOH = 14

Location & Specifications: الاتزان الأيوني، كيمياء 3 ثانوي، التحصيلي، و AP Chemistry.

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Lesson summary

C.1 Simple Harmonic Motion — IB PHYSICS HL notes: Describe oscillations and simple harmonic motion, use the period equations for a mass–spring system and a simple pendulum, and analyse SHM graphs, energy and phase (HL).Oscillation — the repetitive variation with time of the displ…

Displacement x
Amplitude x0
Frequency f
What the symbols mean
Angular frequency ω
Repetitive motion

Part 1 of 10Describing oscillations

Oscillation

Oscillation the repetitive variation with time of the displacement x of an object about its equilibrium position (x = 0)
At equilibrium there is no resultant force

Displacement x

Displacement x a vector in metres measured from equilibrium, positive or negative

Amplitude x0

Amplitude x0 the maximum displacement on either side of equilibrium

Period T

Period T the time for one complete oscillation
A constant period is called isochronous

Frequency f

Frequency f the number of oscillations per second in hertz, f = 1/T
What the symbols mean: T = period, the time for one complete wave (s) · f = frequency (Hz)

Angular frequency ω

Angular frequency ω the rate of change of angular displacement
ω = 2π/T = 2πf in rad s⁻¹
What the symbols mean: ω = angular frequency (rad s⁻¹) · f = frequency (Hz) · T = period (s)

Part 2 of 10Conditions for SHM

Repetitive motion

Repetitive motion back and forth through equilibrium with equal maximum displacement on both sides

Constant period

Constant period every complete vibration takes the same time

Restoring force

Restoring force always directed towards equilibrium and proportional to the distance from it

Defining equation

Defining equation a = −ω²x
What the symbols mean: a = acceleration (m s⁻²) · ω = angular frequency (rad s⁻¹) · x = displacement from equilibrium (m); the minus sign means a always points back to the centre
The minus sign shows a and x are always in opposite directions

Amplitude independence

Amplitude independence the period does not depend on the amplitude for small angles

Not SHM

Not SHM a person on a trampoline, because in the air the restoring force is the constant weight and not proportional to displacement

Part 3 of 10Graphs of SHM

1Starting at equilibrium

Starting at equilibrium x–t is a sine curve, v–t a cosine curve and a–t a negative sine curve

2Starting at the amplitude

Starting at the amplitude x–t is a cosine curve, v–t a negative sine curve and a–t a negative cosine curve

3Phase

Phase x, v and a graphs are each 90° out of phase with the next

4Gradients

Gradients v is the gradient of the x–t graph and a is the gradient of the v–t graph

5Acceleration

Acceleration the a–t graph is the reflection of the x–t graph in the time axis

6Extremes

Extremes acceleration is maximum at x = x₀ where v = 0
Velocity is maximum at equilibrium

Part 4 of 10Mass–spring system

Mass–spring system

Restoring force

F = −kx, Hooke's law

Period

T = 2π√(m/k) for horizontal and vertical systems

Gravity

Gravity the period does not depend on g so it is the same on Earth and the Moon

Stiffness

Stiffness a larger spring constant k gives a shorter period

Mass

Mass a larger mass gives a longer period

Part 5 of 10Simple pendulum

Model

Model a light inextensible string with a point-mass bob attached to a fixed point above equilibrium

Period

T = 2π√(L/g) with L from the pivot to the centre of mass of the bob

Small angles

Small angles valid for amplitudes below about 10° where sin θ ≈ θ

Restoring force

Restoring force the component of weight along the arc

Dependence

Dependence independent of mass and amplitude but dependent on g

Feature	Mass–spring	Simple pendulum
Period	2π√(m/k)	2π√(L/g)
Depends on mass?	Yes	No
Depends on g?	No	Yes
Restoring force	Spring force	Component of weight

Part 6 of 10Energy changes in SHM

1Exchange

Exchange a spring swaps elastic potential energy and kinetic energy
A pendulum swaps gravitational potential energy and kinetic energy

2At the amplitude

At the amplitude potential energy is maximum and kinetic energy is zero

3At equilibrium

At equilibrium kinetic energy is maximum and potential energy is minimum

4Total energy

E = E_P + E_K is constant when there is no damping, by conservation of energy

5Energy–displacement graph

E_P is a U-shaped curve, E_K an n-shaped curve and the total a horizontal line

6Energy–time graph

E_K and E_P vary periodically in opposite directions with two cycles per oscillation
Energy values are never negative

Part 7 of 10Equations of SHM (HL)

Equations of SHM (HL)

From equilibrium

From equilibrium x = x₀ sin ωt, v = ωx₀ cos ωt, a = −ω²x₀ sin ωt

From the amplitude

From the amplitude x = x₀ cos ωt, v = −ωx₀ sin ωt, a = −ω²x₀ cos ωt

Velocity and displacement

Velocity and displacement v = ±ω√(x₀² − x²)

Maximum values

Maximum values v_max = ωx₀ and a_max = ω²x₀

Calculator

Calculator set to radians because ω is in rad s⁻¹

Part 8 of 10Energy equations (HL)

Total energy

E_T = ½mω²x₀²

Potential energy

E_P = ½mω²x²

Kinetic energy

E_K = ½mω²(x₀² − x²)

Link

E_T = E_K,max = E_P,max

Derivation

E_P = E_T − E_K with sin² + cos² = 1
E_K = ½mω²x₀² cos²ωt

Part 9 of 10Phase angle (HL)

1Equation

Equation x = x₀ sin(ωt + φ), v = ωx₀ cos(ωt + φ), a = −ω²x₀ sin(ωt + φ)

2Phase angle φ

Phase angle φ the difference in angular displacement compared with an oscillator that has x = 0 at t = 0
It can vary from 0 to 2π

3Sine and cosine

Sine and cosine they differ by π/2
x₀ sin(ωt + π/2) = x₀ cos ωt

4Graph shift

Graph shift sin(ωt − φ) shifts right by φ and sin(ωt + φ) shifts left by φ

Part 10 of 10More from the specification

1Dynamics of a Mass-Spring System

For a mass-spring system oscillating about equilibrium, Hooke's law provides the restoring force F = -kx, generating an acceleration a = -(k/m)x directly proportional and opposite to displacement.

2Displacement-Time Graph Analysis

The displacement-time graph of simple harmonic motion follows a sinusoidal waveform x(t) = x0 cos(omega t);
- its gradient at any instant yields the instantaneous velocity of the oscillating body.

3Velocity-Time Graph Phase Relationship

The velocity-time graph leads the displacement-time waveform by a phase angle of pi/2 rad (90 degrees), reaching peak speed v_max = omega x0 when displacement is zero.

4Natural Frequency and Period of Oscillation

The time period of an undamped mass-spring oscillator depends strictly on the oscillating mass m and the spring stiffness constant k according to T = 2 pi sqrt(m/k).

5Displacement-time graph

A graph of displacement against time whose gradient is velocity.

6Velocity-time graph

A graph of velocity against time whose gradient is acceleration and area is displacement.

Key terms

Term	Meaning
Simple harmonic motion	Oscillation in which acceleration is proportional to displacement from equilibrium and directed towards the equilibrium position.
Amplitude	The maximum displacement from the equilibrium position.
Period	The time for one complete oscillation.
Frequency	The number of oscillations per unit time.
Angular frequency	ω = 2πf = 2π/T.
Restoring force	A force that always acts towards the equilibrium position.
Phase angle	The angle φ in x = x₀ sin(ωt + φ) that fixes the state of the oscillation at t = 0.

Avoid these mistakes

Saying acceleration and displacement point the same way — in SHM they are always opposite.

Using the pendulum formula for large angles — it needs amplitudes below about 10°.

Thinking the period of a mass–spring system depends on g — it depends only on m and k.

Using a calculator in degrees for ωt — use radians.

Writing E_K = ½mω²x² — that is the potential energy.

Last updated: 15 October 2026

Physics 0625 & 9702 SUVAT Mastery Graph Interpretation

Constant Acceleration Equations (SUVAT) & Slopes

v = u + at | s = ut + ½at² | v² = u² + 2as | s = ½(u + v)t

Displacement-Time Graph: Gradient = Velocity (curve = accelerating).
Velocity-Time Graph: Gradient = Acceleration; Area under curve = Distance travelled / Displacement.
Free Fall in vacuum: a = g ≈ 9.81 m/s² downwards (air resistance negligible).

Part 1 of 10Describing oscillations

Part 2 of 10Conditions for SHM

Part 3 of 10Graphs of SHM

Part 4 of 10Mass–spring system

Part 5 of 10Simple pendulum

Part 6 of 10Energy changes in SHM

Part 7 of 10Equations of SHM (HL)

Part 8 of 10Energy equations (HL)

Part 9 of 10Phase angle (HL)

Part 10 of 10More from the specification

Key terms

Avoid these mistakes

Topic quiz · 33 questionsQuiz for this lesson

Constant Acceleration Equations (SUVAT) & Slopes