MHF4U - GROUP TASK - TPA- THE TRANSFORMED SINUSOIDAL FUNCTION- GROUP
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School
St. Patrick's Higher Secondary School**We aren't endorsed by this school
Course
MTH 32
Subject
Mathematics
Date
Jan 5, 2025
Pages
2
Uploaded by BrigadierOpossumMaster1170
Page 1of 2MHF4UGROUP TASK(2 PARTS) THE TRANSFORMED SINUSOIDAL FUNCTIONInstructions: -No more than 3 students in a group.-All members of a group must participate to complete the following GROUP TASK. Upon completion, the work must be submitted to your classroom teacher. Please make sure all team members names are printed clearly on the finished work. PART-1:Consider the followingtwo (2) transformed sinusoidal functions. For eachone, first complete the tableby writing down values for all shown parameters. Second, sketchthe corresponding graph– showing one(1) full cyclein ?𝑎𝑑𝑖𝑎𝑛?.Showall work on your Team Graph Wall Paper. Remember the mapping: Note: Best to scale the horizontal t- axison your graph in increments of 𝜋 4.ParametersNumerical valueakdcAmplitude (= a)Period (= 2𝜋𝑘)➔𝐲 = −? ?𝐢? [? (? −𝝅?)] + ?➔𝒚 = −? 𝐜?? [? (? −𝝅?)] + ?
Page 2of 2PART-2:Instructions: -Read the word problem. -Based on the given information, sketch the corresponding sinusoidal graph. Use your graph and your knowledge of parameters for a, k, d, & c to produce a sinusoidal equation (cosine or sine). Use your equation to both model the situation and answer questions regarding it. Problem: A weight is bobbing up and down on a spring attached to the ceiling. The bob reaches a maximum height of 100 cm at 4 seconds and then reaches a minimum height of 60 cm at 6 seconds (half period apart). Assume this motion is repetitive, and can be reliably modelled by a sinusoidal function.a)First, plot the Max and Min points on graph paper. Second, determine value of a. Third, determine the Period from graph. Fourth, determine value of k from Period. Fifth, determine values of Phase Shift d and c. b)Use your answers from part-a to determine the Sinusoidal Function which can represent the above situation.c)Use the Sinusoidal Function (your answer from part-b) to predict what height the bob will have at t= 12 seconds.