Read pendulum diagrams in ManYue: count a full return and define length from the pivot

A bob travelling left to right completes only half a cycle in this model. Read original pendulum panels and parameter cards in ManYue, defining pivot, length and same-phase return before applying a small-angle formula. No hanging weights or physical swing experiment is required. The app supports diagrams and location records, not automatic timing, gravity measurement or validation of every real clock against ideal assumptions.

Distinguish pivot, bob and trajectory

Label fixed pivot O, ideal light string and bob centre P, with a dashed arc and vertical equilibrium line. L runs from pivot to ideal point mass; for a finite bob, explicitly approximate using its centre rather than only exposed string. Arc length, pivot height and pendulum length are distinct. Record markers and non-scale scope. Screen centimetres are not real length, and drawn positions need not be simultaneous multiple bobs.

Read a full return across five panels

Draw left extreme A, centre moving right B, right extreme C, centre moving left D and left extreme E in time order. A to E is one period; A to C is half. B/D share position but opposite motion, so not a same-phase return. Supply directions and sequence: one centre image alone cannot establish motion. Equal drawn distances need not imply equal times, and panel counts are neither seconds nor measured speeds.

Attach small-angle and ideal conditions to the formula

Use T=2*pi*sqrt(L/g) with metres and metres per second squared to obtain seconds. It is a small-amplitude approximation for an ideal pendulum with negligible string mass, fixed pivot and omitted resistance, not exact for all angles or real pendulums. Do not use pi equal to three and claim precision, or confuse g with bob mass. Missing L or g supports only a relation, not invented local measurements.

Calculate one metre and one-quarter metre

Assume g nine point eight. At L point two five metre, T is approximately one point zero zero four seconds; at one metre it is approximately two point zero zero seven seconds. Quadrupling length doubles theoretical period. Check the square-root ratio before rounded decimals rather than demand their three-decimal ratio equal exactly two. A fourfold-period answer needs revisiting the square root. If the drawing is not scaled, use the card instead of visual length ratios.

Keep mass and amplitude controls separate

C changes only bob mass with L, g and small-angle conditions fixed. Mass is absent from this ideal period formula, so a heavier drawing does not imply slower motion. D changes amplitude and first checks whether small-angle approximation still applies; it does not establish exact amplitude independence at large angles. Name controls separately rather than change length, size and angle together. Real drag, rotation and stretch need other models; ideal mass independence does not exclude every real mass-related effect.

Check speed clues at extremes and centre

In the ideal undamped model speed is zero instantaneously at extremes and greatest near the centre, not greater merely because farther from centre. Zero speed does not imply zero acceleration or vanished forces; leave force magnitudes outside this note. Distinguish velocity arrows from string direction. Without time data, motion streaks do not measure metres per second. Stylisation can be recorded separately rather than converted into an experimental result.

Check half-period and unit errors in ManYue

Open the original PDF, enlarge panel letters/directions, trace A through E and check length units against the formula card. Twenty-five centimetres must become point two five metre, not twenty-five metres. Separate seconds per cycle from cycles per second. A panel moving to another screen does not change phase boundaries. Share original cards; no hanging-weight measurement is required, and reader navigation time is not pendulum period.

Reopen with one sequence and two calculations

Reopen and reconstruct left-to-right half-cycle, left-to-left full cycle and opposite centre directions before calculating both lengths and their theoretical ratio. Retain pivot-to-centre length, approximation, assumed g, units and rounding, not only a formula. Massive rods, moving pivots or large amplitudes require reassessment. Bookmarks locate material; completion verifies diagram reading and calculation rather than sensor timing or clock calibration.

Related guides and sources

ManYue scene-duration reading: separate panel count from elapsed story time; ManYue clock faces: read minute marks and the hour hand between hours.

Checked on November 15, 2026: Apple public information lists ManYue 2.0.5, requiring iOS / iPadOS 15.0 or later. See the official App Store for published capabilities; verify controls in the installed version.

Method reference: OpenStax: simple pendulums and small-angle period. Materials and numbers are original exercises. Record external reports, paper reasoning and actual reading observations separately, without inventing missing conditions. Sources do not establish new automatic analysis by the app. No step-by-step physical-device, private-server or all-output-environment testing is claimed.