A particular spring has a spring constant of 8. Suppose a 2 kg mass is hung on t

Question

A particular spring has a spring constant of 8. Suppose a 2 kg mass is hung on the spring and is initially sent in motion with an upward velocity of 2 meters per second, 1/2 meter below the equilibrium position.

A) Write down the DE that models the motion of this spring.

B) Write down the initial conditions.

C) Find the equation of motion for the spring.

D) Write the equation of motion in the form x(t) = Asin(wt +b ) or x(t) = Acos(wt +b )      (b= Beta here)

E) How many cycles would the spring - mass system complete in 20pi seconds?

Explanation / Answer

my"+vy'+ky=g(t)

w=2kg,g=9.8,m=2/9.8,v=0,g(t)=0,l=2/8=0.25,k=8

A)ode=(2/9.8)y"+8y=0

B)y(0)=-1/2 meter

y'(0)= -2 meter/s

C)(2/9.8)Y"+8Y=g(t)

e)t=2pisqrt(0.25/9.8)=2pisqrt(5/196)

n=20pi/(2pisqrt(5/196)=10*14/sqrt5=28sqrt5=62.6

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