# EMA 747: Nonlinear and Random Mechanical Vibrations | UW–Madison [View on UW Courses](https://uwcourses.com/courses/EMA_747) ## Dataset ### revision e243353dcb7d79b7247ced91d69443ef4c2a6349 ### repository twangodev/uwcourses ### schema version 6 ### importer version 7 ### projection id 52a78527ff09011d88cb04c7d43867d9fbfec2930bf1dd2ec359ebd2844e0b07 ### observed at 2026-09-07T15:55:43.033547+00:00 ### built at 2026-09-10T19:50:42.743001+00:00 ### courses 8951 ### current instructors 5754 ### limited false ### terms * 1272 * 1264 * 1262 * 1254 * 1252 * 1244 * 1242 * 1234 * 1232 * 1224 * 1222 * 1212 * 1204 * 1202 * 1194 * 1192 * 1184 * 1182 * 1174 * 1172 * 1164 * 1162 * 1154 * 1152 * 1144 * 1142 * 1134 * 1132 * 1124 * 1122 * 1114 * 1112 * 1104 * 1102 * 1094 * 1092 * 1084 * 1082 * 1074 * 1072 ### term 1272 ### departments | subject | count | | --------- | ----- | | AAE | 90 | | ABT | 20 | | ACCTIS | 36 | | ACTSCI | 14 | | AFAERO | 10 | | AFRICAN | 87 | | AFROAMER | 71 | | AGROECOL | 21 | | AMERIND | 53 | | ANAT\&PHY | 7 | | ANATOMY | 2 | | ANESTHES | 8 | | ANSCI | 57 | | ANTHRO | 95 | | ART | 125 | | ARTED | 10 | | ARTHIST | 121 | | ASIALANG | 129 | | ASIAN | 109 | | ASIANAM | 28 | | ASTRON | 38 | | ATMOCN | 69 | | BIOCHEM | 51 | | BIOCORE | 10 | | BIOLOGY | 14 | | BIOMDSCI | 18 | | BME | 66 | | BMI | 41 | | BMOLCHEM | 10 | | BOTANY | 69 | | BSE | 44 | | C\&ESOC | 73 | | CBE | 48 | | CHEM | 101 | | CHICLA | 52 | | CIVENGR | 133 | | CLASSICS | 47 | | CNP | 10 | | CNSRSCI | 50 | | COMARTS | 137 | | COMPBIO | 15 | | COMPLIT | 11 | | COMPSCI | 138 | | COUNPSY | 78 | | CRB | 19 | | CS\&D | 71 | | CSCS | 40 | | CURRIC | 193 | | DANCE | 93 | | DERM | 8 | | DS | 88 | | DYSCI | 35 | | ECE | 155 | | ECON | 145 | | EDPOL | 114 | | EDPSYCH | 97 | | ELPA | 70 | | EMA | 53 | | EMERMED | 17 | | ENGL | 206 | | ENTOM | 40 | | ENVIRST | 148 | | EP | 15 | | EPD | 67 | | ESL | 16 | | F\&WECOL | 60 | | FAMMED | 22 | | FINANCE | 50 | | FOLKLORE | 40 | | FOODSCI | 43 | | FRENCH | 63 | | 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| NEUROL | 7 | | NEURSURG | 4 | | NTP | 11 | | NURSING | 111 | | NUTRSCI | 65 | | OBS\&GYN | 18 | | OCCTHER | 39 | | ONCOLOGY | 14 | | OPHTHALM | 5 | | OTM | 43 | | PATH | 34 | | PATH-BIO | 29 | | PEDIAT | 26 | | PHARMACY | 31 | | PHILOS | 77 | | PHMCOL-M | 11 | | PHMPRAC | 45 | | PHMSCI | 60 | | PHYASST | 37 | | PHYSICS | 88 | | PHYSIOL | 3 | | PHYTHER | 37 | | PLANTSCI | 52 | | PLPATH | 35 | | POLISCI | 192 | | POPHLTH | 58 | | PORTUG | 33 | | PSYCH | 101 | | PSYCHIAT | 22 | | PUBAFFR | 54 | | PUBLHLTH | 23 | | RADIOL | 11 | | REALEST | 41 | | RELIGST | 90 | | RHABMED | 9 | | RMI | 24 | | RP\&SE | 102 | | S\&APHM | 17 | | SCANDST | 73 | | SLAVIC | 89 | | SOC | 149 | | SOCWORK | 87 | | SOILSCI | 46 | | SPANISH | 83 | | SRMED | 21 | | STAT | 94 | | STDYABRD | 52 | | STS | 8 | | SURGERY | 25 | | SURGSCI | 33 | | THEATRE | 91 | | URBRPL | 60 | | UROLOGY | 5 | | ZOOLOGY | 89 | ## course ### run id 20260907T155543-ce3781c4 ### semester 1272 ### observed at 2026-09-07 15:55:43.033547+00:00 ### record version id 7c4dd8554d6655d2212e56751a8362c4bc3320f631473bf867f402060afb1de9 ### course id EMA 747 ### course uid course\_d07ca4cbc01d8803ebe79374 ### catalog version id 6298dd364b3cac2d2bbf368fa9e02124d70b27932e61f9b358550f3256c5e79c ### course number 747 ### subjects * EMA ### title NONLINEAR AND RANDOM MECHANICAL VIBRATIONS ### description Exact solutions and sectorial linearization; free and forced vibration of mechanical systems with nonlinear restoring force; self-excited mechanical vibrations and relaxation vibrations; subharmonic responses; nonlinear vibration of mechanical systems with more than one degree of freedom; nonlinear vibration of bounded continuous media; random excitation and random response, random vibrations of mechanical systems and structures; random vibrations of nonlinear mechanical systems; failure of materials under random vibrations. ### requirements text Graduate/professional standing ### credit offering ids None recorded. ### llm job id enrich-8b774950c2b6adfdc46d1b82 ### llm output id 81b6f5d5527027cc92534438b356a2b3ecddd67c791019bef91df992d6e54ecb ### llm model nvidia/Qwen3.6-35B-A3B-NVFP4 ### llm model revision 1355db6a052410cfd62085d94b58866fd0f2c3c5 ### llm task version 14 ### llm search status valid ### llm summary Covers exact solutions, sectorial linearization, and analysis of nonlinear and random mechanical vibrations. ### llm topics * Nonlinear restoring forces * Self-excited and relaxation vibrations * Subharmonic responses * Multi-degree-of-freedom systems * Bounded continuous media * Random excitation and response * Material failure under random vibrations ### llm skills * Applying exact solutions and sectorial linearization techniques * Analyzing free and forced vibrations in nonlinear mechanical systems * Investigating self-excited and relaxation vibrations * Examining subharmonic responses in mechanical systems * Modeling nonlinear vibrations in multi-degree-of-freedom systems * Analyzing nonlinear vibrations in bounded continuous media * Evaluating random excitation and response in mechanical systems and structures * Studying random vibrations in nonlinear mechanical systems ### llm assumed background None recorded. ### llm search phrases * nonlinear vibration mechanical systems * random excitation response * sectorial linearization * self-excited vibrations * subharmonic responses ### llm requirements status valid ### llm student summary status valid ### llm experience status insufficient\_evidence ### catalog variants None recorded. ### student summary #### context hash 29d50bc420cab9bb07bdd3d74ee42f4460418f6b71e3b0812e2d22408aebf828 #### course id EMA 747 #### current instructors None recorded. #### difficulty workload None recorded. #### errors None recorded. #### historical context None recorded. #### message No course-specific reviews available #### offered false #### profile hash 5cb4dabf887cdbcd8c00d5a1312e10828b95c63f30bc3ea76aea199565390d02 #### quick take Recent recorded grades — Spring 2017: 3.75 GPA, 83.3% A/AB (n=6 letter grades); Spring 2019: 3.68 GPA, 84.2% A/AB (n=19 letter grades); Fall 2025: 3.93 GPA, 100.0% A/AB (n=7 letter grades). ```json { "citations": [ { "course_id": "EMA 747", "run_id": "20260907T155543-ce3781c4", "source_record": { "entity_id": "5777d960-0a1c-3ab2-9b89-02d6cb86bffa", "file": "tables/observations.parquet", "kind": "grades", "source": "madgrades" }, "table": "grades_latest", "term_id": "1174", "type": "grade" }, { "course_id": "EMA 747", "run_id": "20260907T155543-ce3781c4", "source_record": { "entity_id": "5777d960-0a1c-3ab2-9b89-02d6cb86bffa", "file": "tables/observations.parquet", "kind": "grades", "source": "madgrades" }, "table": "grades_latest", "term_id": "1194", "type": "grade" }, { "course_id": "EMA 747", "run_id": "20260907T155543-ce3781c4", "source_record": { "entity_id": "5777d960-0a1c-3ab2-9b89-02d6cb86bffa", "file": "tables/observations.parquet", "kind": "grades", "source": "madgrades" }, "table": "grades_latest", "term_id": "1262", "type": "grade" } ] } ``` #### student experience None recorded. #### task hash 74fb0997943e888960bbc9e47db8c4fd12e4292d55c20509d8d89db6a9910f68 #### teaching history None recorded. #### term id 1272 #### term name 2026 Fall #### version 2 ### requirements #### nodes ```json [ { "children": [], "condition": "Graduate/professional standing", "course": null, "evidence": "Graduate/professional standing", "id": "n0", "kind": "condition" } ] ``` #### notes None recorded. #### root n0 #### status parsed ### instructors None recorded. ### offerings None recorded. ### sections None recorded. ### grade instructors ```json [ { "instructor_uid": "instructor_08e2340ec7d61ceaeca8c162", "source": "madgrades", "source_instructor_id": "4275262", "identity_basis": "source_id", "identity_status": "source_identified", "name": "MATTHEW ALLEN", "email": null, "first_observed_at": "2026-09-06 23:14:58.172943+00:00", "last_observed_at": "2026-09-07 15:55:43.033547+00:00", "ratings": { "review_count": 2, "quality": 4.5, "difficulty": 3, "quality_count": 2, "difficulty_count": 2, "profile_id": "rmp:2068863", "source_url": "https://www.ratemyprofessors.com/professor/2068863", "match_basis": "exact_name", "observed_at": "2026-09-07 16:19:54.350363+00:00", "courses": {}, "bayesian_quality": 3.7360779850423596, "prior_mean": 3.6596857835465957, "prior_weight": 20 }, "grade_statistics": { "gpa": 3.465, "graded": 258, "counts": [ 129, 57, 38, 13, 14, 4, 3 ], "sections": 105 }, "instructor_url": "/instructors/MATTHEW_ALLEN" }, { "instructor_uid": "instructor_6634b7c2d5ff08a7ed5226d3", "source": "madgrades", "source_instructor_id": "6689172", "identity_basis": "source_id", "identity_status": "source_identified", "name": "THOMAS BREUNUNG", "email": null, "first_observed_at": "2026-09-06 23:14:58.172943+00:00", "last_observed_at": "2026-09-07 15:55:43.033547+00:00", "grade_statistics": { "gpa": 3.294, "graded": 34, "counts": [ 12, 9, 5, 5, 2, 1, 0 ], "sections": 10 }, "instructor_url": "/instructors/THOMAS_BREUNUNG--instructor_6634b7c2d5ff08a7ed5226d3" } ] ``` ### grades ```json [ { "run_id": "20260907T155543-ce3781c4", "semester": "1272", "observed_at": "2026-09-07 15:55:43.033547+00:00", "course_id": "EMA 747", "course_uid": "course_d07ca4cbc01d8803ebe79374", "term_id": "1174", "term_name": "Spring 2017", "instructors": [ "MATTHEW ALLEN" ], "a": 5, "ab": 0, "b": 0, "bc": 1, "c": 0, "d": 0, "f": 0, "satisfactory": 1, "unsatisfactory": 0, "credit": 0, "no_credit": 0, "passed": 0, "incomplete": 1, "no_work": 0, "not_reported": 0, "other": 0, "total": 8, "source_aliases": [ "EMA 747" ] }, { "run_id": "20260907T155543-ce3781c4", "semester": "1272", "observed_at": "2026-09-07 15:55:43.033547+00:00", "course_id": "EMA 747", "course_uid": "course_d07ca4cbc01d8803ebe79374", "term_id": "1194", "term_name": "Spring 2019", "instructors": [ "MATTHEW ALLEN" ], "a": 14, "ab": 2, "b": 1, "bc": 0, "c": 2, "d": 0, "f": 0, "satisfactory": 0, "unsatisfactory": 0, "credit": 0, "no_credit": 0, "passed": 0, "incomplete": 0, "no_work": 0, "not_reported": 0, "other": 0, "total": 19, "source_aliases": [ "EMA 747" ] }, { "run_id": "20260907T155543-ce3781c4", "semester": "1272", "observed_at": "2026-09-07 15:55:43.033547+00:00", "course_id": "EMA 747", "course_uid": "course_d07ca4cbc01d8803ebe79374", "term_id": "1262", "term_name": "Fall 2025", "instructors": [ "Thomas Breunung" ], "a": 6, "ab": 1, "b": 0, "bc": 0, "c": 0, "d": 0, "f": 0, "satisfactory": 0, "unsatisfactory": 0, "credit": 0, "no_credit": 0, "passed": 0, "incomplete": 0, "no_work": 0, "not_reported": 0, "other": 0, "total": 7, "source_aliases": [ "EMA 747" ] } ] ``` ### statistics #### gpa 3.75 #### graded 32 #### counts * 25 * 3 * 1 * 1 * 2 * 0 * 0 ### grade conflicts None recorded. ### evidence #### history * 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| | 0.8–1.2 | 0 | false | | 1.2–1.6 | 0 | false | | 1.6–2.0 | 0 | false | | 2.0–2.4 | 1 | false | | 2.4–2.8 | 14 | false | | 2.8–3.2 | 263 | false | | 3.2–3.6 | 735 | false | | 3.6–4.0 | 1360 | true | #### departments ```json [ { "subject": "EMA", "comparison": { "size": 13, "gpaPercentile": 92, "countPercentile": 0, "medianCount": 89, "histogram": [ { "range": "0.0–0.4", "count": 0, "current": false }, { "range": "0.4–0.8", "count": 0, "current": false }, { "range": "0.8–1.2", "count": 0, "current": false }, { "range": "1.2–1.6", "count": 0, "current": false }, { "range": "1.6–2.0", "count": 0, "current": false }, { "range": "2.0–2.4", "count": 0, "current": false }, { "range": "2.4–2.8", "count": 1, "current": false }, { "range": "2.8–3.2", "count": 3, "current": false }, { "range": "3.2–3.6", "count": 5, "current": false }, { "range": "3.6–4.0", "count": 4, "current": true } ] } } ] ``` ### terms #### 1174 ##### term 1174 ##### gpa 3.75 ##### count 6 ##### departments | subject | comparison | | ------- | ---------- | | EMA | | #### 1194 ##### term 1194 ##### gpa 3.6842105263157894 ##### count 19 ##### departments | subject | comparison | | ------- | ---------- | | EMA | | #### 1262 ##### term 1262 ##### gpa 3.9285714285714284 ##### count 7 ##### departments | subject | comparison | | ------- | ---------- | | EMA | | ### benchmarks #### all ##### school ###### size 2373 ###### gpa 3.612636146949807 ###### top Share 79.04360363370581 ###### count 80 ##### EMA ###### size 13 ###### gpa 3.3738195033149774 ###### top Share 63.2568291308756 ###### count 89 #### terms ##### 1174 ###### school ###### size 955 ###### gpa 3.4597947384071412 ###### top Share 69.5290038366363 ###### count 69 ##### 1194 ###### school ###### size 1040 ###### gpa 3.4906527436719808 ###### top Share 71.74728845515045 ###### count 67 ##### 1262 ###### school ###### size 1320 ###### gpa 3.628825763035853 ###### top Share 80.21118846327654 ###### count 70 ## instructor Trends ```json [ { "uid": "instructor_08e2340ec7d61ceaeca8c162", "name": "MATTHEW ALLEN", "count": 25, "terms": [ { "term": "1174", "count": 6, "sections": 1, "gpa": 3.75 }, { "term": "1194", "count": 19, "sections": 1, "gpa": 3.6842105263157894 } ] }, { "uid": "instructor_6634b7c2d5ff08a7ed5226d3", "name": "THOMAS BREUNUNG", "count": 7, "terms": [ { "term": "1262", "count": 7, "sections": 1, "gpa": 3.9285714285714284 } ] } ] ``` ## following None recorded.