Pre-Calc/Trig Unit 2: Circular Functions/4.5 Harmonic Motion Find frequency and period Solve the problem.
The position of a weight attached to a spring is «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»s«/mi»«mo»(«/mo»«mi»t«/mi»«mo»)«/mo»«mo»=«/mo»«mo»#«/mo»«mi»a«/mi»«mo»§#160;«/mo»«mi»cos«/mi»«mo»§#160;«/mo»«mo»#«/mo»«mi»b«/mi»«mo»§#160;«/mo»«mi»t«/mi»«/math» inches after t seconds. What are the frequency and period of the system?

]]> 1.0000000 0.3333333 0 0 frequency=#fperiod=#p]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mfrac><mi>b</mi><mrow><mn>2</mn><mo>*</mo><pi/></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mfrac><mrow><mn>2</mn><mo>*</mo><pi/></mrow><mi>b</mi></mfrac></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mi>r</mi><mi mathvariant="normal">e</mi><mi>q</mi><mi>u</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi>c</mi><mi>y</mi><mo>=</mo><mo>#</mo><mi>f</mi><mspace linebreak="newline"/><mi>p</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi mathvariant="normal">i</mi><mi>o</mi><mi mathvariant="normal">d</mi><mo>=</mo><mo>#</mo><mi>p</mi></math>]]></correctAnswer><correctAnswer id="1"></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution">50/50</data><data name="inputField">popupEditor</data><data name="casSession">null</data></localData></question> Maximum distance from equilibrium Solve the problem.

The position of a weight attached to a spring is «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»s«/mi»«mo»(«/mo»«mi»t«/mi»«mo»)«/mo»«mo»=«/mo»«mo»#«/mo»«mi»a«/mi»«mo»§#160;«/mo»«mi»cos«/mi»«mo»§#160;«/mo»«mo»(«/mo»«mo»#«/mo»«mi»b«/mi»«mo»§#160;«/mo»«mi mathvariant=¨normal¨»§#960;«/mi»«mo»§#160;«/mo»«mi mathvariant=¨normal¨»t«/mi»«mo»)«/mo»«/math» inches after t seconds. What is the maximum height that the weight rises above the equilibrium position?

]]> 1.0000000 0.3333333 0 0 #answer]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>answer</mi><mo>=</mo><mfenced close="|" open="|"><mi>a</mi></mfenced></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>a</mi><mi>ns</mi><mi>w</mi><mi mathvariant="normal">e</mi><mi>r</mi></math>]]></correctAnswer><correctAnswer id="1"></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m, y, z, a, f, p, n, µ, d, da, h, G, T, P, E, Z, Y</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession">null</data></localData></question> Solve the problem.A guitar string is plucked so that it vibrates with a ... Solve the problem.

A guitar string is plucked so that it vibrates with a frequency of

Suppose the maximum displacement at the center of the string is

Find an equation of the form

to model this displacement. Round constants to 2 decimal places.

]]> 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1.0000000 0.3333333 0 true true ABCD s(t) = 0.55 cos 464.96t

]]> Correct

]]> s(t) = 1.10 cos 464.96t

]]> Incorrect

]]> s(t) = 0.55 cos 11.78t

]]> Incorrect

]]> s(t) = 1.10 cos 11.78t

]]> Incorrect

]]> Answer not given

]]> Solve the problem.A weight attached to a spring is pulled down 5 inches ... Solve the problem.

A weight attached to a spring is pulled down 5 inches below the equilibrium position. Assuming that the period of the system is

second, determine a trigonometric model that gives the position of the weight at time t seconds.]]> 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 1.0000000 0.3333333 0 true true abc s(t) = -5cos 6πt Correct s(t) = 5cos 6πt Incorrect s(t) = -5cos 3πt Incorrect t]]> 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 Incorrect Solve the problem.The formula for the up and down motion of a weight on a ... Solve the problem.

The formula for the up and down motion of a weight on a spring is given by

If the spring constant is 5, then what mass m must be used in order to produce a period of 4 seconds?]]> 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1.0000000 0.3333333 0 true true abc ]]> 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Correct ]]> 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Incorrect ]]> 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Incorrect ]]> 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Incorrect