(33%) Problem 3: An object oscillates with an angular frequency = 6 rad s. At t
ID: 1883003 • Letter: #
Question
(33%) Problem 3: An object oscillates with an angular frequency = 6 rad s. At t = 0, the object 1s atx,-4.5 . It is moving with velocity vd-14 cm s 1n the positive x-direction. The position of the obiect can be described through the equation x(t) = A cos(at 33% Part (a) What is the the phase constant of the oscillation in radians? (Caution: If you are using the trig functions in the palette below be careful to adjust the setting between degrees and radians as needed.) Grade Summa Deductions Potential rv 0% 10096 cosO 7 8 9 tan() | acosO Sin Submissions Attempts remaining: 20 (096 per attempt) detailed view cotan asin0 atan acotan sinhO cosh0tanh cotanhO END Degrees Radians N0 Submit Hint I give up! Hints: 296 deduction per hint. Hints remaining: 5 Feedback: 0% deduction per feedback. 33% Part (b) Write an equation for the amplitude A of the oscillation in terms ofx0 and .Use the phase shift as a system parameter. 33% Part (c) Calculate the value of the amplitude A of the oscillation in cmExplanation / Answer
Solution:
a)
V = -Awsin(wt+phi) .........(i)
x = Acos(wt + phi)...........(ii)
dividing equation i / ii
V / x = -w * tan(wt + phi)
=> 14 / 4.5 = - 6 tan(phi) at t=0
=> phi = tan^-1( -0.5185)
=> phi = -0.4783 rad
b) given x = A cos(wt + phi)
for t = 0 , x0 = A cos(phi)
A = x0 / cos(phi) is the required answer.
c) A = 4.5 / cos(-0.4783)
=> A = 5.0688 cm is the required answer.
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