Question

(17%) Problem 1: An object oscillates with an angular frequency o = 3 rad/s. At 1-0, the object is at xo = 3.5 cm. It is moving with velocity vx0= 2 cm/s in the positive x-direction. The position of the object can be described through the equation x() = A cos(o1+). 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 Summary Deductions 0% Potential 100% Submissions Attempts remaining: 8 (6% per attempt) detailed view sin() cos) tan() ( ) 7 8 9 TOME cotan) asino acos TEM 4 5 6 atan acotan sinh * 1 2 3 : Cosh) | tanh0 | cotanh) | | |-| 0 | | HND • Degrees Radians VO BACKSPACE DEL CLEAR Submit Hint Feedback I give up! Ilints: 2% deduction per hint. Ilints remaining: 5 Feedback: 2% deduction per feedback. A 33% Part (b) Write an equation for the amplitude A of the oscillation in terms of xo and . Use the phase shift as a system parameter. A 33% Part (c) Calculate the value of the amplitude A of the oscillation in cm.

Answer 1

Any Cuiven wa rode Xo = 3.5cm at tzo { = 2 anys A / NAX at tao x (2) z A cog (wf+0) - Here ae (+)-portion of object A amplitude w y angulon acceleration 6 & phan angle. At tzo, from egno. x = A cº 8 ( (4=b) +b) or no a Acoso - elifferential equation 10 with respect to 't'. de 2 A (-sinfrotto] w 2 - Aw sinetto) [: sino = V1-1080] a cop (14 th) = x de = -Aw/ T-ca8240ft 8) = -WANT- League o = - WAJA?d? - wraz sez - (0821 otto) = -1 A Onn i rays =-/3rad/kr) JA²_ (3.5 any 2 or (0.667 cm) 2 = (-/A2_12125) ? or 0.4444 cm2 a A2 - 12.25 ame or A2 x 12.7 cm Az 3.563 cm ry

A cool wolto) o alt). At to Hoa Alo88 - or co$¢ to 2 $ 2009+ ( a $ 2 0084 ( 3-560 ) a $10.79º ang ready or 16 20.108 mod ) Ane ② from equation . Y AL 305 am Cos 10.79 or [A2 3.563 am] Are TA 23.563 am