{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-08-14T00:13:02.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2026-08-14T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":44704,"title":"Damping of Servomotors with Tachometer Feedback","description":"In Control Engineering, servomotors with tachometer feedback can be modeled by the second order system\r\n\r\n K / [J*s^2 + (B + K*K_v)*s + K] \r\n\r\nDepending on the damping ratio of the servomotor, the system can be classified as underdamped, critically damped or overdamped. In this problem, you will be given the following as input:\r\n\r\nB - damping of servomotor (viscous and friction elements)\r\n\r\nJ - inertia of servomotor\r\n\r\nK - gain of proportional controller\r\n\r\nK_v - velocity feedback constant of tachometer \r\n\r\nYou are to correctly classify the system by returning either ' _underdamped_ ', ' _critical_ ' or ' _overdamped_ '.","description_html":"\u003cp\u003eIn Control Engineering, servomotors with tachometer feedback can be modeled by the second order system\u003c/p\u003e\u003cpre\u003e K / [J*s^2 + (B + K*K_v)*s + K] \u003c/pre\u003e\u003cp\u003eDepending on the damping ratio of the servomotor, the system can be classified as underdamped, critically damped or overdamped. In this problem, you will be given the following as input:\u003c/p\u003e\u003cp\u003eB - damping of servomotor (viscous and friction elements)\u003c/p\u003e\u003cp\u003eJ - inertia of servomotor\u003c/p\u003e\u003cp\u003eK - gain of proportional controller\u003c/p\u003e\u003cp\u003eK_v - velocity feedback constant of tachometer\u003c/p\u003e\u003cp\u003eYou are to correctly classify the system by returning either ' \u003ci\u003eunderdamped\u003c/i\u003e ', ' \u003ci\u003ecritical\u003c/i\u003e ' or ' \u003ci\u003eoverdamped\u003c/i\u003e '.\u003c/p\u003e","function_template":"function damp = ServoDamp(B,J,K,K_v)\r\n % damp?   \r\n  switch B \u003e B_c     %Critical damping\r\n      case 1\r\n          'underdamped'\r\n      case 2\r\n          'critical'\r\n      case 3\r\n          'overdamped'\r\n  end\r\nend","test_suite":"%%\r\nB = 1; J = 1; K = 12.5; K_v = 0.1;\r\nassert(isequal(ServoDamp(B,J,K,K_v),'underdamped'))\r\n\r\n%%\r\nB = 2; J = 1; K = 4; K_v = 0.5;\r\nassert(isequal(ServoDamp(B,J,K,K_v),'critical'))\r\n\r\n%%\r\nB = 1; J = 1; K = 12.5; K_v = 0.5;\r\nassert(isequal(ServoDamp(B,J,K,K_v),'overdamped'))\r\n\r\n%%\r\nB = 2; J = 2; K = 8; K_v = 0.75;\r\nassert(isequal(ServoDamp(B,J,K,K_v),'critical'))\r\n\r\n%%\r\nB = 2; J = 2; K = 10; K_v = 0.75;\r\nassert(isequal(ServoDamp(B,J,K,K_v),'overdamped'))\r\n\r\n%%\r\nB = 1; J = 2; K = 10; K_v = 0.75;\r\nassert(isequal(ServoDamp(B,J,K,K_v),'underdamped'))\r\n\r\n%%\r\nB = rand; J = 2; K = 10; K_v = 0.75;\r\nassert(isequal(ServoDamp(B,J,K,K_v),'underdamped'))\r\n\r\n%%\r\nB = rand; J = 2; K = 10; K_v = 1;\r\nassert(isequal(ServoDamp(B,J,K,K_v),'overdamped'))\r\n\r\n%%\r\nB = rand; J = 1; K = 10; K_v = 1;\r\nassert(isequal(ServoDamp(B,J,K,K_v),'overdamped'))\r\n\r\n%%\r\nB = 3; J = 3; K = 3; K_v = 1;\r\nassert(isequal(ServoDamp(B,J,K,K_v),'critical'))\r\n\r\n%%\r\nB = 4; J = 4; K = 4; K_v = 1;\r\nassert(isequal(ServoDamp(B,J,K,K_v),'critical'))","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":178544,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":44,"test_suite_updated_at":"2018-08-02T17:30:44.000Z","rescore_all_solutions":false,"group_id":67,"created_at":"2018-08-01T23:16:46.000Z","updated_at":"2026-05-25T00:51:24.000Z","published_at":"2018-08-02T08:43:51.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn Control Engineering, servomotors with tachometer feedback can be modeled by the second order system\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ K / [J*s^2 + (B + K*K_v)*s + K]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDepending on the damping ratio of the servomotor, the system can be classified as underdamped, critically damped or overdamped. In this problem, you will be given the following as input:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eB - damping of servomotor (viscous and friction elements)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eJ - inertia of servomotor\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eK - gain of proportional controller\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eK_v - velocity feedback constant of tachometer\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou are to correctly classify the system by returning either '\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eunderdamped\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e ', '\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ecritical\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e ' or '\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eoverdamped\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e '.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"}],"problem_search":{"problems":[{"id":44704,"title":"Damping of Servomotors with Tachometer Feedback","description":"In Control Engineering, servomotors with tachometer feedback can be modeled by the second order system\r\n\r\n K / [J*s^2 + (B + K*K_v)*s + K] \r\n\r\nDepending on the damping ratio of the servomotor, the system can be classified as underdamped, critically damped or overdamped. In this problem, you will be given the following as input:\r\n\r\nB - damping of servomotor (viscous and friction elements)\r\n\r\nJ - inertia of servomotor\r\n\r\nK - gain of proportional controller\r\n\r\nK_v - velocity feedback constant of tachometer \r\n\r\nYou are to correctly classify the system by returning either ' _underdamped_ ', ' _critical_ ' or ' _overdamped_ '.","description_html":"\u003cp\u003eIn Control Engineering, servomotors with tachometer feedback can be modeled by the second order system\u003c/p\u003e\u003cpre\u003e K / [J*s^2 + (B + K*K_v)*s + K] \u003c/pre\u003e\u003cp\u003eDepending on the damping ratio of the servomotor, the system can be classified as underdamped, critically damped or overdamped. In this problem, you will be given the following as input:\u003c/p\u003e\u003cp\u003eB - damping of servomotor (viscous and friction elements)\u003c/p\u003e\u003cp\u003eJ - inertia of servomotor\u003c/p\u003e\u003cp\u003eK - gain of proportional controller\u003c/p\u003e\u003cp\u003eK_v - velocity feedback constant of tachometer\u003c/p\u003e\u003cp\u003eYou are to correctly classify the system by returning either ' \u003ci\u003eunderdamped\u003c/i\u003e ', ' \u003ci\u003ecritical\u003c/i\u003e ' or ' \u003ci\u003eoverdamped\u003c/i\u003e '.\u003c/p\u003e","function_template":"function damp = ServoDamp(B,J,K,K_v)\r\n % damp?   \r\n  switch B \u003e B_c     %Critical damping\r\n      case 1\r\n          'underdamped'\r\n      case 2\r\n          'critical'\r\n      case 3\r\n          'overdamped'\r\n  end\r\nend","test_suite":"%%\r\nB = 1; J = 1; K = 12.5; K_v = 0.1;\r\nassert(isequal(ServoDamp(B,J,K,K_v),'underdamped'))\r\n\r\n%%\r\nB = 2; J = 1; K = 4; K_v = 0.5;\r\nassert(isequal(ServoDamp(B,J,K,K_v),'critical'))\r\n\r\n%%\r\nB = 1; J = 1; K = 12.5; K_v = 0.5;\r\nassert(isequal(ServoDamp(B,J,K,K_v),'overdamped'))\r\n\r\n%%\r\nB = 2; J = 2; K = 8; K_v = 0.75;\r\nassert(isequal(ServoDamp(B,J,K,K_v),'critical'))\r\n\r\n%%\r\nB = 2; J = 2; K = 10; K_v = 0.75;\r\nassert(isequal(ServoDamp(B,J,K,K_v),'overdamped'))\r\n\r\n%%\r\nB = 1; J = 2; K = 10; K_v = 0.75;\r\nassert(isequal(ServoDamp(B,J,K,K_v),'underdamped'))\r\n\r\n%%\r\nB = rand; J = 2; K = 10; K_v = 0.75;\r\nassert(isequal(ServoDamp(B,J,K,K_v),'underdamped'))\r\n\r\n%%\r\nB = rand; J = 2; K = 10; K_v = 1;\r\nassert(isequal(ServoDamp(B,J,K,K_v),'overdamped'))\r\n\r\n%%\r\nB = rand; J = 1; K = 10; K_v = 1;\r\nassert(isequal(ServoDamp(B,J,K,K_v),'overdamped'))\r\n\r\n%%\r\nB = 3; J = 3; K = 3; K_v = 1;\r\nassert(isequal(ServoDamp(B,J,K,K_v),'critical'))\r\n\r\n%%\r\nB = 4; J = 4; K = 4; K_v = 1;\r\nassert(isequal(ServoDamp(B,J,K,K_v),'critical'))","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":178544,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":44,"test_suite_updated_at":"2018-08-02T17:30:44.000Z","rescore_all_solutions":false,"group_id":67,"created_at":"2018-08-01T23:16:46.000Z","updated_at":"2026-05-25T00:51:24.000Z","published_at":"2018-08-02T08:43:51.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn Control Engineering, servomotors with tachometer feedback can be modeled by the second order system\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ K / [J*s^2 + (B + K*K_v)*s + K]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDepending on the damping ratio of the servomotor, the system can be classified as underdamped, critically damped or overdamped. In this problem, you will be given the following as input:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eB - damping of servomotor (viscous and friction elements)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eJ - inertia of servomotor\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eK - gain of proportional controller\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eK_v - velocity feedback constant of tachometer\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou are to correctly classify the system by returning either '\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eunderdamped\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e ', '\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ecritical\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e ' or '\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eoverdamped\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e '.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"}],"errors":[],"facets":[[{"value":"Functions II","count":1,"selected":false}],[{"value":"medium","count":1,"selected":false}]],"term":"tag:\"damping ratio\"","page":1,"per_page":50,"sort":"map(difficulty_value,0,0,999) asc"}}