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(11%) Problem 2: A mass m = 1.4 kg hangs at the end of a vertical spring whose top end is fixed to the ceiling. The spring has spring constant k = 95 N/m and negligible mass. The mass undergoes simple harmonic motion when placed in vertical motion, with its position given as a function of time by y(t) = A cos(@t-o), with the positive y-axis pointing upward. At time t=0 the mass is observed to be at a distance d=0.35 m below its equilibrium height with an upward speed of vo = 3 m/s.
20% Part (a) Find the angular frequency of the oscillation, in radians per second. @=8.23 ✓ Correct! ► 20% Part (b) Find the value of o, in radians. o = sin() cos() cotan() asin() atan() acotan() cosh() A=-0.35 A = -0.35 X Attempts Remain tan() л () 7 8 acos() E 4 5 sinh() cotanh() tanh() Degrees O Radians Submit Hint Hints: 2 for a 0% deduction. Hints remaining: 0 -Find the velocity as a function of time, v(t). Then substitute t=0 to obtain expressions for yo=y(0) and vo= v(0). Eliminate A from the two equations and solve for p in terms of w, yo, and vo -Consider how the velocity function is obtained from the position function. 20% Part (c) Calculate the value of A, in meters. V 9 6 1 2 3 لیا + 0 VO BACKSPACE DEL HOME END CLEAR Feedback I give up! Feedback: 0% deduction per feedback. 20% Part (d) What is the mass's velocity along the y-axis, in meters per second, at time t₁ = 0.25 s? v(t)=2.54 x Attempts Remain 20% Part (e) What is the magnitude of the mass's maximum acceleration, in meters per second squared?