A mass weighing 8 pounds stretches a spring 3 in. The mass is initially released from a point 6 inches below the equilibrium position with an upward velocity of 2 ft/s. a) Find the equation of motion. (Use the convention that displacements measured below the equilibrium position are positive.) y .5cos(8√(2)t)-1/(4√(2))sin(8√(2)t) b) The equation of motion from part (a) should have the form y(t) = C1cos(ωt) + C2sin(ωt). Write the equation of motion in the from y(t) = Asin(ωt + φ), where A = √((C1)2 + (C2)2) and tan(φ) = C1/C2 y=√(128.25)sin(8√(2)t+2.53) c) What is the velocity of the mass when t = 3π/2 seconds? In which direction is the mass heading at this instant? 71.9 ft/s heading u
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5. A mass weighing 8 pounds stretches a spring 3 in. The mass is initially released from a point 6 inches below the
equilibrium position with an upward velocity of 2 ft/s.
a) Find the equation of motion. (Use the convention that displacements measured below the equilibrium position
are positive.) y .5cos(8√(2)t)-1/(4√(2))sin(8√(2)t)
b) The equation of motion from part (a) should have the form y(t) = C1cos(ωt) + C2sin(ωt). Write the equation of
motion in the from y(t) = Asin(ωt + φ), where A = √((C1)2 + (C2)2) and tan(φ) = C1/C2 y=√(128.25)sin(8√(2)t+2.53)
c) What is the velocity of the mass when t = 3π/2 seconds? In which direction is the mass heading at this instant? 71.9 ft/s heading up
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