Question

A 189-kg mass, when attached to the end of a spring hanging vertically, stretches the spring 9 m. The mass is in a medium that exerts a viscous resistance of 3024 N when the mass has a velocity of 4 m/sec. Assume the mass is given an initial velocity of 14 m/s from the equilibrium position. a) Determine the spring constant k. Use g = 10 m/sec. k b) Determine the damping coeffient 7. 7 c) If the initial value problem for y(t), where y(t) denotes the displacement (in meters) of the mass from its equilibrium rest position, can be written in the form my'' + yy' + ky = 0 where y(0) = yo and y' (0) = y's what are the values of yo and yo? Yo yo d) Solve it only far enough to describe the motion of the system with the terminology of this course. The system is e) What value of the damping coefficient y is required for the system to be critically damped? No decimals. Use "sqrt(foo)", without quotes, if you need the square root of foo. 7

Answer 1

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ma 189k9 2- 9m ng = kx ke 189 x 10 9 210 N/m Answer a Ka 210 Nim fue - YoV : -yu V: 3024 4 Y : 756 N-5/m Answeb so equation of motion my' + xy'tky - Initially maii is given an intial velocuts of rum/s from the equillibrium position Ansawal So Yo=0 y'(o)= iu mis 7 Wo damping combank 210 756 WE damping constant = 2x189 - 2 . Wo: 1.054-1 So. Natural angular frequency> damping constent So. The system is underdamped e for the system to be critically damped Wo 2m

지 m 내 ys 2M m 2/km 2 2018 2. : 398.u