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.1.3 Time Period of a Mass–Spring System — IB Physics HL Revision Notes & Topical Questions

5 min read 10 parts Lesson 5 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.1.3 Time Period of a Mass–Spring System — IB PHYSICS SL notes: Use T = 2π√(m/k) to find the period of a mass on a spring and explain what affects it.System — a mass m on a light spring of spring constant k oscillates horizontally on a smooth surface or hangs verticallyHooke's l…

Hooke's law
Newton's second law
Comparison
Rearranged form
Both orientations
Equilibrium

Part 1 of 8The mass–spring system

The mass–spring system

System

System a mass m on a light spring of spring constant k oscillates horizontally on a smooth surface or hangs vertically

Hooke's law

Hooke's law the spring force is F = −kx, where x is the extension or compression from the natural length
k is in newtons per metre (N m⁻¹).
The minus sign shows the force opposes the displacement.

SHM

F = −kx is the restoring force that makes the motion simple harmonic (C.1.2)

Part 2 of 8Deriving the period

Newton's second law

Newton's second law ma = −kx, so a = −(k/m)x

Comparison

Comparison with a = −ω²x this gives ω² = k/m

Period

T = 2π√(m/k), where T is in s, m in kg and k in N m⁻¹

Frequency

Frequency f = (1/2π)√(k/m)

Rearranged form

Rearranged form k = 4π²mf²

Both orientations

Both orientations the equation applies to horizontal and vertical systems

Part 3 of 8What affects the period

Mass

T ∝ √m, so four times the mass doubles the period
A heavier object is harder to accelerate.

Spring constant

T ∝ 1/√k, so a stiffer spring gives a shorter period
A larger k gives a larger restoring force.

Amplitude

Amplitude it has no effect while Hooke's law holds
The spring must not be stretched beyond its elastic limit.

Gravity

Gravity the period is independent of g, so the same system oscillates with the same period on Earth and on the Moon
Gravity changes the equilibrium position, not the period.

Part 4 of 8Vertical springs

Equilibrium

Equilibrium the weight is balanced by the spring force, mg = ke, where e is the static extension

Motion about it

Motion about it displacing the mass by x from the new equilibrium gives net force −kx, so it is SHM with the same formula

Static extension

Static extension k/m = g/e, so T = 2π√(e/g)

Tension

Tension the spring must stay under tension throughout, because a slack spring cannot supply a restoring force

Part 5 of 8Experiments with a spring

Hang different masses from the spring and measure the extension for each.

Plot weight against extension; the gradient is k.

For several masses, time 10 or more oscillations and divide to find T.

Plot T² against m.

Result

T² = (4π²/k)m gives a straight line through the origin with gradient 4π²/k

Timing

Timing timing 10 or more oscillations reduces the percentage uncertainty due to reaction time

Limit

Limit if a force–extension graph curves at large loads, the limit of proportionality is passed and the SHM equations no longer apply

Part 6 of 8Springs in combination

Springs in combination

Two identical springs in parallel

Two identical springs in parallel they share the load, so the effective constant is 2k
The period is shorter by a factor of √2.

Two identical springs in series

Two identical springs in series the effective constant is k/2
The period is longer by a factor of √2.

Trolley between two springs

Trolley between two springs both springs act on it, so the effective constant is 2k

Part 7 of 8Assumptions and refinements

Light spring

Light spring the formula assumes a spring of negligible mass and negligible friction

Spring with mass

Spring with mass the effective oscillating mass is about m + m_s/3

Damping

Damping air resistance makes the amplitude decay but leaves the period almost unchanged

Natural frequency

Natural frequency the frequency from f = (1/2π)√(k/m) is the natural frequency of the system, used in resonance

Part 8 of 8More from the specification

Key terms

Term	Meaning
Spring constant k	Force per unit extension, in N m⁻¹.
Hooke's law	Force is proportional to extension within the elastic limit.
Restoring force	F = −kx directed to the equilibrium position.
Static extension	Extension of a vertical spring when the mass is at rest.
Elastic limit	The extension beyond which the spring does not return to its original length.

Avoid these mistakes

Using mg alone as the spring constant — k = F/x needs the extension in metres.

Thinking the amplitude affects the period.

Saying a different value of g changes the period of a mass–spring system — it does not.

Writing T = 2π√(k/m) with the ratio inverted.

Using centimetres for the extension without converting to metres.

Last updated: 15 October 2026