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It must be directly proportional to the displacement from the equilibrium position ($F \\propto -x$).
It must act in the opposite direction to the displacement.

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IB Physics C.1.1 Defining and Analyzing Simple Harmonic Motion Flashcards

Topic A - Space, time and motion

A.1 Kinematics4 subtopics

A.2 Forces and momentum4 subtopics

A.3 Work, energy and power3 subtopics

A.4 Rigid body mechanics (HL only)3 subtopics

A.5 Galilean and special relativity (HL only)4 subtopics

Topic B - The particulate nature of matter

B.1 Thermal energy transfers3 subtopics

B.2 Greenhouse effect2 subtopics

B.3 Gas laws2 subtopics

B.4 Thermodynamics (HL only)3 subtopics

B.5 Current and circuits5 subtopics

Topic C - Wave behaviour

C.1 Simple harmonic motion3 subtopics

C.2 Wave model2 subtopics

C.3 Wave phenomena3 subtopics

C.4 Standing waves and resonance4 subtopics

C.5 Doppler effect2 subtopics

Topic D - Fields

D.1 Gravitational fields4 subtopics

D.2 Electric and magnetic fields4 subtopics

D.3 Motion in electromagnetic fields3 subtopics

D.4 Induction (HL only)2 subtopics

Topic E - Nuclear and quantum physics

E.1 Structure of the atom4 subtopics

E.2 Quantum physics (HL only)2 subtopics

E.3 Radioactive decay3 subtopics

E.4 Fission2 subtopics

E.5 Fusion and stars3 subtopics