The second part please chrs MIni C www.webassign.net/web/Student/Assignme Respon

Question

The second part please

chrs MIni C www.webassign.net/web/Student/Assignme Response /last? dep 15893757 R Google D Bleach 515 Read B D Adventure Holidays Booking Confirmation D https//blackboard-vs A Edit Profile 11. 112 points. I Previous Answers was ZillDiffEQModAp10 5.1.013 My Notes Ask Your Teacher Under some circumstances when two para el springs, with constants k and k support a single mass, the effective spring constant of the system is given by k k1 k2. A mass weighing 20 pounds stretches one spring 3 inches and another spring 4 inches. The springs are attached to a common rigid support and then to a metal plate. As shown in the figure, the mass is attached to the center of the plate in the double-spring arrangement. 20 lb Determine the effective spring constant of this system. K 140 tially released from the equilibrium position with a downward velocity of 8 ft/s. (Use 32 ft/se for the acceleration due to Find the equation of mot (t f the mass is in g gravity.) x(t) 622 PM 4 Ask me anything 3/10/2017 R4

Explanation / Answer

The problem can be solved as follows -

Force equation for the 1st spring -

f=kx

k1=f/x

or, k1=20/(3/12) lb/ft

or, k1 = 80 lb/ft.

Like-wise -

k2= 20 / (4/12) lb/ft. = 60 lb/ft.

so, K=4k1k2/(k1+k2)

=> k = (4*80*60) / (80+60) = 137 lb/ft

[Please check the answer of your first part]

Now, find out the equation of motion -

m*d2x/dt2= -kx

or, 20/32* d2x/dt2= -137x

or, d2x/dt2 + 219x=0

therefore, w2= 219

=> w = 14.8

Now -

x(t)= c1coswt + c2sinwt

differentiating and using v(0)= 8 ft/s and x(0)=0

c1=0, c2 = 8/14.8 = 0.54

Hence the requisite equation -

x(t)= (0.54)sin(14.8t).

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