// Numbas version: exam_results_page_options
{"name": "Amplitude, period and phase shift (from graph)", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Amplitude, period and phase shift (from graph)", "tags": [], "metadata": {"description": "<p>given plot of a graph. find amplitude, period and phase shift</p>", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "<p>What are the period, amplitude and phase shift (<strong>from $y=sinx^o$</strong>) of the graph shown below?</p>\n<p></p>\n<p>If needed you can zoom and pan the graph to find suitable points.</p>\n<p></p>\n<p>{geogebra_applet('https://www.geogebra.org/m/uetnepha',defs)}</p>", "advice": "<ul>\n<li>The amplitude is the vertical height of the graph from the central line to the highest point. In this case that equals $\\var{a}$.</li>\n</ul>\n<p></p>\n<ul>\n<li>The period is the time for one wave. This is the distance from a point on the curve to the equivalent next time it occurs along the graph. The easiest way to do this is to look at points along the axis. For this graph one point is at $(\\simplify{0-{c}},0)$. Moving to the right, the next equivalent point is at $(\\simplify{{period}-{c}},0)$. The $x$ distance between these two points and hence the period is $\\var{period}$</li>\n</ul>\n<p></p>\n<ul>\n<li>The phase shift is how far to the left or right the point $(0,0)$ from the graph $y=sinx$ has moved. In this case the point $(0,0)$ has moved $\\var{abs_c}$ units to the $\\var{L_R}$ so the phase shift is $\\simplify{0-{c}}$.</li>\n</ul>", "rulesets": {}, "extensions": ["geogebra"], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(1..3)", "description": "", "templateType": "anything", "can_override": false}, "defs": {"name": "defs", "group": "Ungrouped variables", "definition": "[\n['a',a],\n  ['b',b],\n  ['c',c]\n  ]", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(0.2,0.3,0.4,0.5,0.6,0.8,0.9,1,1.2,1.5,1.6,1.8,2)", "description": "", "templateType": "anything", "can_override": false}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "random(-40,-35,-30,-25,-20,-15,-10,-5,5,10,15,20,25,30,35,40)", "description": "", "templateType": "anything", "can_override": false}, "abs_c": {"name": "abs_c", "group": "Ungrouped variables", "definition": "abs({c})", "description": "", "templateType": "anything", "can_override": false}, "Left": {"name": "Left", "group": "Ungrouped variables", "definition": "\"left\"", "description": "", "templateType": "string", "can_override": false}, "right": {"name": "right", "group": "Ungrouped variables", "definition": "\"right\"", "description": "", "templateType": "string", "can_override": false}, "L_R": {"name": "L_R", "group": "Ungrouped variables", "definition": "if(c<0,right,left)", "description": "", "templateType": "anything", "can_override": false}, "period": {"name": "period", "group": "Ungrouped variables", "definition": "360/b", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "b", "c", "defs", "abs_c", "Left", "right", "L_R", "period"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<ul>\n<li>Give the exact value for all answers (you should get an integer)</li>\n<li>Do not write units in the answer</li>\n<li>For the phase shift you need to write for example $-20$ or $10$. Do not use the words left of right.</li>\n</ul>\n<p></p>\n<p>Amplitude [[0]]</p>\n<p>period [[2]]</p>\n<p>phase shift [[1]]</p>\n<p></p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "amp", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{a}", "maxValue": "{a}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "phase", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "-{c}", "maxValue": "-{c}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "sigfig", "precision": "1", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "per", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "360/{b}", "maxValue": "360/{b}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "sigfig", "precision": "3", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Mike Phipps", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/14139/"}]}]}], "contributors": [{"name": "Mike Phipps", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/14139/"}]}