{"id":347,"date":"2025-09-13T01:47:37","date_gmt":"2025-09-13T01:47:37","guid":{"rendered":"https:\/\/learn-by-animation.com\/?page_id=347"},"modified":"2025-09-13T01:50:10","modified_gmt":"2025-09-13T01:50:10","slug":"proportional-patterns-in-oscillations","status":"publish","type":"page","link":"https:\/\/learn-by-animation.com\/?page_id=347","title":{"rendered":"Proportional Patterns in Oscillations"},"content":{"rendered":"\n

Comprehensive Proportionality Patterns in Oscillations and Waves<\/strong><\/h3>\n\n\n\n
Relationship\/Concept<\/td>Proportionality Pattern<\/td>Governing Formula\/Concept<\/td>Explanation<\/td><\/tr>
Fundamental Concepts of Oscillation<\/strong><\/td><\/td><\/td><\/td><\/tr>
Frequency vs. Period<\/td>Frequency is inversely proportional<\/strong> to the period. (v \u221d 1\/T)<\/td>v = 1\/T<\/td>If the time for one oscillation (period) is doubled, the number of oscillations per second (frequency) is halved.<\/td><\/tr>
Angular Frequency vs. Period<\/td>Angular frequency is inversely proportional<\/strong> to the period. (\u03c9 \u221d 1\/T)<\/td>\u03c9 = 2\u03c0 \/ T<\/td>A system with a long period of oscillation has a small angular frequency.<\/td><\/tr>
Simple Harmonic Motion (SHM): Dynamics and Kinematics<\/strong><\/td><\/td><\/td><\/td><\/tr>
Restoring Force vs. Displacement<\/td>Restoring force is directly proportional<\/strong> to displacement (and in the opposite direction). (F \u221d -x)<\/td>F = -kx<\/td>The farther an object is displaced from its equilibrium, the stronger the force pulling it back.<\/td><\/tr>
Acceleration vs. Displacement<\/td>Acceleration is directly proportional<\/strong> to displacement (and in the opposite direction). (a \u221d -x)<\/td>a(t) = -\u03c9\u00b2x(t)<\/td>The magnitude of acceleration is zero at the equilibrium position and maximum at the extreme points of displacement.<\/td><\/tr>
Maximum Velocity vs. Amplitude<\/td>Maximum velocity is directly proportional<\/strong> to the amplitude. (v_max \u221d A)<\/td>v_max = \u03c9A<\/td>If the amplitude of oscillation doubles, the maximum speed reached by the object also doubles (for a constant \u03c9).<\/td><\/tr>
Maximum Acceleration vs. Amplitude<\/td>Maximum acceleration is directly proportional<\/strong> to the amplitude. (a_max \u221d A)<\/td>a_max = \u03c9\u00b2A<\/td>Doubling the amplitude of oscillation doubles the maximum acceleration experienced by the object (for a constant \u03c9).<\/td><\/tr>
Energy in Simple Harmonic Motion<\/strong><\/td><\/td><\/td><\/td><\/tr>
Total Energy vs. Amplitude<\/td>Total energy is proportional to the square<\/strong> of the amplitude. (E \u221d A\u00b2)<\/td>E = (1\/2)kA\u00b2<\/td>If the amplitude of oscillation is doubled, the total energy of the system increases by a factor of four.<\/td><\/tr>
Kinetic Energy vs. Velocity<\/td>Kinetic energy is proportional to the square<\/strong> of the velocity. (K \u221d v\u00b2)<\/td>K = (1\/2)mv\u00b2<\/td>Kinetic energy is maximum when velocity is maximum (at the equilibrium position) and zero at the extreme points where velocity is momentarily zero.<\/td><\/tr>
Potential Energy vs. Displacement<\/td>Potential energy is proportional to the square<\/strong> of the displacement. (U \u221d x\u00b2)<\/td>U = (1\/2)kx\u00b2<\/td>Potential energy is maximum at the extreme points of displacement and zero at the equilibrium position.<\/td><\/tr>
Specific Oscillating Systems<\/strong><\/td><\/td><\/td><\/td><\/tr>
Period of Spring-Mass System vs. Mass<\/td>The period is proportional to the square root<\/strong> of the mass. (T \u221d \u221am)<\/td>T = 2\u03c0\u221a(m\/k)<\/td>To double the period of oscillation for a given spring, you must increase the mass by a factor of four.<\/td><\/tr>
Period of Spring-Mass System vs. Spring Constant<\/td>The period is inversely proportional to the square root<\/strong> of the spring constant. (T \u221d 1\/\u221ak)<\/td>T = 2\u03c0\u221a(m\/k)<\/td>A stiffer spring (larger k) will cause the mass to oscillate with a shorter period.<\/td><\/tr>
Period of Simple Pendulum vs. Length<\/td>The period is proportional to the square root<\/strong> of its length. (T \u221d \u221aL)<\/td>T = 2\u03c0\u221a(L\/g)<\/td>To double the time it takes for a pendulum to complete one swing, its length must be quadrupled. The period is independent of the bob’s mass.<\/td><\/tr>
Period of Simple Pendulum vs. Gravity<\/td>The period is inversely proportional to the square root<\/strong> of the acceleration due to gravity. (T \u221d 1\/\u221ag)<\/td>T = 2\u03c0\u221a(L\/g)<\/td>A pendulum of a given length will have a longer period (swing slower) on the Moon than on Earth because the Moon’s gravity is weaker.<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

——-<\/p>\n\n\n\n

Relationship\/Concept<\/td>Proportionality Pattern<\/td>Governing Formula\/Concept (Chain of Logic)<\/td>Explanation\/Context<\/td><\/tr>
Core SHM & Energy Relationships<\/strong><\/td><\/td><\/td><\/td><\/tr>
Period of Spring-Mass System vs. Spring Stiffness<\/td>Period is inversely proportional to the square root<\/strong> of the spring constant. (T \u221d 1\/\u221ak)<\/td>T = 2\u03c0\u221a(m\/k)<\/td>A stiffer spring (higher k) results in a faster oscillation and therefore a shorter period.<\/td><\/tr>
Stored Potential Energy vs. Spring Stiffness<\/td>For a given displacement, potential energy is directly proportional<\/strong> to the spring constant. (U \u221d k)<\/td>U = (1\/2)kx\u00b2<\/td>A stiffer spring stores more energy for the same amount of stretch or compression.<\/td><\/tr>
Kinetic Energy vs. Potential Energy<\/td>Kinetic energy is inversely related<\/strong> to potential energy during oscillation.<\/td>E_total = K + U = constant<\/td>As the oscillator moves away from equilibrium, kinetic energy is converted into potential energy. As it moves toward equilibrium, the reverse happens.<\/td><\/tr>
Frequency of a Pendulum vs. Length<\/td>Frequency is inversely proportional to the square root<\/strong> of the length. (f \u221d 1\/\u221aL)<\/td>f = 1\/T and T = 2\u03c0\u221a(L\/g)<\/td>A short pendulum swings back and forth more frequently (has a higher pitch if it makes a sound) than a long pendulum.<\/td><\/tr>
Wave Properties (Derived from Oscillations)<\/strong><\/td><\/td><\/td><\/td><\/tr>
Frequency vs. Wavelength (for a constant wave speed)<\/td>Frequency is inversely proportional<\/strong> to wavelength. (f \u221d 1\/\u03bb)<\/td>v_wave = f\u03bb, so f = v_wave\/\u03bb<\/td>For sound waves traveling in air (constant speed), high-frequency sounds (high pitch) have short wavelengths.<\/td><\/tr>
Wave Speed in a String vs. Tension<\/td>Wave speed is proportional to the square root<\/strong> of the tension. (v \u221d \u221aF_T)<\/td>v = \u221a(F_T \/ \u03bc) (where \u03bc is mass per unit length)<\/td>Tightening a guitar string (increasing tension) increases the speed of the wave, which in turn increases its fundamental frequency (pitch).<\/td><\/tr>
Fundamental Frequency of a String vs. Tension<\/td>Frequency is proportional to the square root<\/strong> of the tension. (f \u221d \u221aF_T)<\/td>Combines f \u221d v (from v=f\u03bb) and v \u221d \u221aF_T<\/td>This is why tuning a guitar by tightening the strings raises the pitch of the notes.<\/td><\/tr>
Quantum & Electromagnetic Wave Relationships<\/strong><\/td><\/td><\/td><\/td><\/tr>
Energy of a Photon vs. Frequency<\/td>Energy is directly proportional<\/strong> to frequency. (E \u221d f)<\/td>E = hf (Planck’s relation)<\/td>This is a cornerstone of quantum mechanics. Higher frequency electromagnetic waves, like UV light, carry more energy per photon than lower frequency waves, like radio waves.<\/td><\/tr>
Energy of a Photon vs. Wavelength<\/strong><\/td>Energy is inversely proportional<\/strong> to wavelength. (E \u221d 1\/\u03bb)<\/td>E = hf and f = c\/\u03bb \u2192 E = hc\/\u03bb<\/td>This is a highly useful derived relationship. High-energy gamma rays have extremely short wavelengths, while low-energy radio waves have very long wavelengths.<\/td><\/tr>
Momentum of a Photon vs. Frequency<\/td>Momentum is directly proportional<\/strong> to frequency. (p \u221d f)<\/td>p = E\/c and E = hf \u2192 p = hf\/c<\/td>Photons of higher frequency light will impart more momentum upon impact.<\/td><\/tr>
de Broglie Wavelength of a Particle vs. Momentum<\/td>Wavelength is inversely proportional<\/strong> to momentum. (\u03bb \u221d 1\/p)<\/td>\u03bb = h\/p<\/td>This is the principle of wave-particle duality. A fast-moving particle (high momentum) exhibits a shorter wavelength. This is fundamental to electron microscopes.<\/td><\/tr>
Damped & Driven Oscillations<\/strong><\/td><\/td><\/td><\/td><\/tr>
Amplitude of Damped Oscillation vs. Time<\/td>Amplitude decays exponentially<\/strong> with time.<\/td>A(t) = A\u2080e^(-bt\/2m)<\/td>The energy of the oscillator is lost to friction or drag, causing the amplitude of swings to get progressively smaller.<\/td><\/tr>
Rate of Energy Loss vs. Damping Factor<\/td>The rate of energy loss is proportional to the square<\/strong> of the velocity and directly proportional<\/strong> to the damping constant. (P_loss \u221d b v\u00b2)<\/td>F_damping = -bv, Power = F \u00b7 v<\/td>A thicker fluid (higher b) or faster motion will dissipate the oscillator’s energy more quickly.<\/td><\/tr>
Amplitude at Resonance vs. Damping Factor<\/td>The maximum amplitude at resonance is inversely proportional<\/strong> to the damping factor. (A_max \u221d 1\/b)<\/td>Derived from the amplitude equation for driven oscillators.<\/td>A system with very low damping (like a crystal glass) can shatter from resonance because the amplitude can grow to destructive levels.<\/td><\/tr>
Sharpness of Resonance Peak vs. Damping<\/td>The sharpness of the resonance peak is inversely proportional<\/strong> to damping.<\/td>A high “Q factor” (Quality factor) means low damping and a sharp, narrow resonance peak.<\/td>Systems with low damping are very sensitive to being driven at a specific frequency (e.g., a radio tuner).<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

Proportionality Comparisons for MCQs in Oscillations<\/strong><\/h3>\n\n\n\n

This table shows the ratio between two systems (System 2 vs. System 1) when a single parameter is changed.<\/p>\n\n\n\n

System \/ Property<\/td>Parameter Changed<\/td>Resulting Proportional Change<\/td>Ratio Formula for Calculation<\/td><\/tr>
1. Spring-Mass System<\/strong><\/td><\/td><\/td><\/td><\/tr>
Period (T)<\/td>Mass<\/strong> (m) is changed.<\/td>Period is proportional to the square root<\/strong> of mass.<\/td>T\u2082 \/ T\u2081 = \u221a(m\u2082 \/ m\u2081)<\/td><\/tr>
Period (T)<\/td>Spring Constant<\/strong> (k) is changed.<\/td>Period is inversely<\/strong> proportional to the square root<\/strong> of the spring constant.<\/td>T\u2082 \/ T\u2081 = \u221a(k\u2081 \/ k\u2082)<\/td><\/tr>
Frequency (v)<\/td>Mass<\/strong> (m) is changed.<\/td>Frequency is inversely<\/strong> proportional to the square root<\/strong> of mass.<\/td>v\u2082 \/ v\u2081 = \u221a(m\u2081 \/ m\u2082)<\/td><\/tr>
Frequency (v)<\/td>Spring Constant<\/strong> (k) is changed.<\/td>Frequency is proportional to the square root<\/strong> of the spring constant.<\/td>v\u2082 \/ v\u2081 = \u221a(k\u2082 \/ k\u2081)<\/td><\/tr>
2. Simple Pendulum<\/strong><\/td><\/td><\/td><\/td><\/tr>
Period (T)<\/td>Length<\/strong> (L) is changed.<\/td>Period is proportional to the square root<\/strong> of length.<\/td>T\u2082 \/ T\u2081 = \u221a(L\u2082 \/ L\u2081)<\/td><\/tr>
Period (T)<\/td>Gravity<\/strong> (g) is changed (e.g., Earth vs. Moon).<\/td>Period is inversely<\/strong> proportional to the square root<\/strong> of gravity.<\/td>T\u2082 \/ T\u2081 = \u221a(g\u2081 \/ g\u2082)<\/td><\/tr>
Frequency (v)<\/td>Length<\/strong> (L) is changed.<\/td>Frequency is inversely<\/strong> proportional to the square root<\/strong> of length.<\/td>v\u2082 \/ v\u2081 = \u221a(L\u2081 \/ L\u2082)<\/td><\/tr>
3. Energy in SHM<\/strong><\/td><\/td><\/td><\/td><\/tr>
Total Energy (E)<\/td>Amplitude<\/strong> (A) is changed.<\/td>Energy is proportional to the square<\/strong> of the amplitude.<\/td>E\u2082 \/ E\u2081 = (A\u2082 \/ A\u2081)\u00b2<\/td><\/tr>
Total Energy (E)<\/td>Frequency<\/strong> (v) or Angular Frequency<\/strong> (\u03c9) is changed.<\/td>Energy is proportional to the square<\/strong> of the frequency.<\/td>E\u2082 \/ E\u2081 = (v\u2082 \/ v\u2081)\u00b2 = (\u03c9\u2082 \/ \u03c9\u2081)\u00b2<\/td><\/tr>
Total Energy (E)<\/td>Spring Constant<\/strong> (k) is changed (for the same amplitude).<\/td>Energy is directly proportional<\/strong> to the spring constant.<\/td>E\u2082 \/ E\u2081 = k\u2082 \/ k\u2081<\/td><\/tr>
Amplitude (A)<\/td>Energy<\/strong> (E) is changed (for the same oscillator).<\/td>Amplitude is proportional to the square root<\/strong> of the energy.<\/td>A\u2082 \/ A\u2081 = \u221a(E\u2082 \/ E\u2081)<\/td><\/tr>
4. Kinematics of SHM (Velocity & Acceleration)<\/strong><\/td><\/td><\/td><\/td><\/tr>
Max Velocity (v_max)<\/td>Amplitude<\/strong> (A) is changed (at same frequency).<\/td>Max velocity is directly proportional<\/strong> to the amplitude.<\/td>v_max\u2082 \/ v_max\u2081 = A\u2082 \/ A\u2081<\/td><\/tr>
Max Velocity (v_max)<\/td>Frequency<\/strong> (v) is changed (at same amplitude).<\/td>Max velocity is directly proportional<\/strong> to the frequency.<\/td>v_max\u2082 \/ v_max\u2081 = v\u2082 \/ v\u2081<\/td><\/tr>
Max Acceleration (a_max)<\/td>Amplitude<\/strong> (A) is changed (at same frequency).<\/td>Max acceleration is directly proportional<\/strong> to the amplitude.<\/td>a_max\u2082 \/ a_max\u2081 = A\u2082 \/ A\u2081<\/td><\/tr>
Max Acceleration (a_max)<\/td>Frequency<\/strong> (v) is changed (at same amplitude).<\/td>Max acceleration is proportional to the square<\/strong> of the frequency.<\/td>a_max\u2082 \/ a_max\u2081 = (v\u2082 \/ v\u2081)\u00b2<\/td><\/tr>
Max Acceleration (a_max)<\/td>Displacement<\/strong> (x) from equilibrium is changed.<\/td>Acceleration is directly proportional<\/strong> to the displacement.<\/td>a\u2082 \/ a\u2081 = x\u2082 \/ x\u2081<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

<\/p>\n\n\n\n

Here are the key variations of the question you provided, structured in a format perfect for MCQ practice.<\/p>\n\n\n\n

Variations of SHM Formulas for MCQs<\/strong><\/h3>\n\n\n\n

The table is organized by the quantity being asked for. Each row represents a potential multiple-choice question.<\/p>\n\n\n\n

If you are given…<\/td>And you are asked for…<\/td>The answer is…<\/td>How to derive it<\/td><\/tr>
Category 1: Finding Maximum Speed (v_max)<\/strong><\/td><\/td><\/td><\/td><\/tr>
Amplitude (A<\/strong>) and Period (T<\/strong>)<\/td>Maximum Speed (v_max)<\/strong><\/td>2\u03c0A \/ T<\/strong><\/td>Start with v_max = \u03c9A and substitute \u03c9 = 2\u03c0\/T.<\/td><\/tr>
Amplitude (A<\/strong>) and Frequency (v<\/strong>)<\/td>Maximum Speed (v_max)<\/strong><\/td>2\u03c0vA<\/strong><\/td>Start with v_max = \u03c9A and substitute \u03c9 = 2\u03c0v.<\/td><\/tr>
Amplitude (A<\/strong>), Mass (m<\/strong>), and Spring Constant (k<\/strong>)<\/td>Maximum Speed (v_max)<\/strong><\/td>A\u221a(k\/m)<\/strong><\/td>Start with v_max = \u03c9A and substitute \u03c9 = \u221a(k\/m).<\/td><\/tr>
Total Energy (E<\/strong>) and Mass (m<\/strong>)<\/td>Maximum Speed (v_max)<\/strong><\/td>\u221a(2E\/m)<\/strong><\/td>Use the energy formula E = \u00bdmv_max\u00b2 and solve for v_max.<\/td><\/tr>
Max Acceleration (a_max<\/strong>) and Amplitude (A<\/strong>)<\/td>Maximum Speed (v_max)<\/strong><\/td>\u221a(a_max \u22c5 A)<\/strong><\/td>Combine v_max\u00b2 = \u03c9\u00b2A\u00b2 and a_max = \u03c9\u00b2A to get v_max\u00b2 = a_max \u22c5 A.<\/td><\/tr>
Max Acceleration (a_max<\/strong>) and Angular Frequency (\u03c9<\/strong>)<\/td>Maximum Speed (v_max)<\/strong><\/td>a_max \/ \u03c9<\/strong><\/td>Rearrange a_max = \u03c9 \u22c5 v_max (since \u03c9\u00b2A = \u03c9 \u22c5 \u03c9A).<\/td><\/tr>
Category 2: Finding Maximum Acceleration (a_max)<\/strong><\/td><\/td><\/td><\/td><\/tr>
Amplitude (A<\/strong>) and Period (T<\/strong>)<\/td>Maximum Acceleration (a_max)<\/strong><\/td>4\u03c0\u00b2A \/ T\u00b2<\/strong><\/td>Start with a_max = \u03c9\u00b2A and substitute \u03c9 = 2\u03c0\/T.<\/td><\/tr>
Amplitude (A<\/strong>) and Frequency (v<\/strong>)<\/td>Maximum Acceleration (a_max)<\/strong><\/td>4\u03c0\u00b2v\u00b2A<\/strong><\/td>Start with a_max = \u03c9\u00b2A and substitute \u03c9 = 2\u03c0v.<\/td><\/tr>
Max Speed (v_max<\/strong>) and Period (T<\/strong>)<\/td>Maximum Acceleration (a_max)<\/strong><\/td>2\u03c0v_max \/ T<\/strong><\/td>Combine a_max = \u03c9v_max and \u03c9 = 2\u03c0\/T.<\/td><\/tr>
Max Force (F_max<\/strong>) and Mass (m<\/strong>)<\/td>Maximum Acceleration (a_max)<\/strong><\/td>F_max \/ m<\/strong><\/td>Use Newton’s second law, F = ma.<\/td><\/tr>
Spring Constant (k<\/strong>), Amplitude (A<\/strong>), and Mass (m<\/strong>)<\/td>Maximum Acceleration (a_max)<\/strong><\/td>kA \/ m<\/strong><\/td>Combine F_max = kA and F_max = ma_max, then solve for a_max.<\/td><\/tr>
Category 3: Finding Period (T) or Frequency (v)<\/strong><\/td><\/td><\/td><\/td><\/tr>
Mass (m<\/strong>) and Spring Constant (k<\/strong>)<\/td>Period (T)<\/strong><\/td>2\u03c0\u221a(m\/k)<\/strong><\/td>Start with \u03c9 = \u221a(k\/m) and use T = 2\u03c0\/\u03c9.<\/td><\/tr>
Max Speed (v_max<\/strong>) and Amplitude (A<\/strong>)<\/td>Period (T)<\/strong><\/td>2\u03c0A \/ v_max<\/strong><\/td>Rearrange the formula v_max = 2\u03c0A \/ T.<\/td><\/tr>
Max Acceleration (a_max<\/strong>) and Amplitude (A<\/strong>)<\/td>Period (T)<\/strong><\/td>2\u03c0\u221a(A\/a_max)<\/strong><\/td>Start with a_max = \u03c9\u00b2A, solve for \u03c9, then find T.<\/td><\/tr>
Max Acceleration (a_max<\/strong>) and Max Speed (v_max<\/strong>)<\/td>Period (T)<\/strong><\/td>2\u03c0v_max \/ a_max<\/strong><\/td>Start with a_max = \u03c9v_max, solve for \u03c9 = a_max\/v_max, then find T.<\/td><\/tr>
Category 4: Finding Total Energy (E)<\/strong><\/td><\/td><\/td><\/td><\/tr>
Mass (m<\/strong>), Amplitude (A<\/strong>), and Period (T<\/strong>)<\/td>Total Energy (E)<\/strong><\/td>2m\u03c0\u00b2A\u00b2 \/ T\u00b2<\/strong><\/td>Start with E = \u00bdm\u03c9\u00b2A\u00b2 and substitute \u03c9 = 2\u03c0\/T.<\/td><\/tr>
Spring Constant (k<\/strong>) and Amplitude (A<\/strong>)<\/td>Total Energy (E)<\/strong><\/td>\u00bdkA\u00b2<\/strong><\/td>This is a fundamental energy formula for a spring.<\/td><\/tr>
Mass (m<\/strong>) and Max Speed (v_max<\/strong>)<\/td>Total Energy (E)<\/strong><\/td>\u00bdmv_max\u00b2<\/strong><\/td>The total energy equals the maximum kinetic energy.<\/td><\/tr><\/tbody><\/table><\/figure>\n","protected":false},"excerpt":{"rendered":"

Comprehensive Proportionality Patterns in Oscillations and Waves Relationship\/Concept Proportionality Pattern Governing Formula\/Concept Explanation Fundamental Concepts of Oscillation Frequency vs. Period Frequency is inversely proportional to the period. (v \u221d 1\/T) v = 1\/T If the time for one oscillation (period) is doubled, the number of oscillations per second (frequency) is halved. Angular Frequency vs. Period […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-347","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/learn-by-animation.com\/index.php?rest_route=\/wp\/v2\/pages\/347","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/learn-by-animation.com\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/learn-by-animation.com\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/learn-by-animation.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/learn-by-animation.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=347"}],"version-history":[{"count":2,"href":"https:\/\/learn-by-animation.com\/index.php?rest_route=\/wp\/v2\/pages\/347\/revisions"}],"predecessor-version":[{"id":351,"href":"https:\/\/learn-by-animation.com\/index.php?rest_route=\/wp\/v2\/pages\/347\/revisions\/351"}],"wp:attachment":[{"href":"https:\/\/learn-by-animation.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=347"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}