A student gets a 2.5 kg mass to oscillate up and down on bottom of a light verti

Question

A student gets a 2.5 kg mass to oscillate up and down on bottom of a light vertical spring by pulling her hand up and down on the top end of the spring. The                spring is a real spring with a spring constant of 84 N/m and a damping constant of 0.7 N sec/m.                 

1) At what approximate frequency should the student move her hand up and down to get the maximum motion from the mass with the minimum motion of her                            hand?                             

f hando = ____________ sec^-1                             

2) The student now stops moving her hand and the mass slowly comes to rest. How long after she stop shaking her hand will it take for the                                amplitude of the mass to reach one half its maximum amplitude?                             

t1/2= ______________ Seconds

Explanation / Answer

a) Frequency= 1/T = 1/(2*pi) (sqrt(k/m) =

given:
k= 84 N/m
m= 2.4 kg

1/(2*pi) (sqrt(84/2.4))= 0.94/sec

2.)After she lets go, we have a free damped oscillation. The differential equation in this case is:

2.8

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