A mass m=4 is attached to both a spring with spring constant k=145 and a dash-pot...

A mass m=4 is attached to both a spring with spring constant k=145 and a dash-pot with damping constant c=4.

The ball is started in motion with initial position x₀=1 and initial velocity v₀=6 .
Determine the position function x(t) .

x(t)=?

Note that, in this problem, the motion of the spring is underdamped, therefore the solution can be written in the form x(t)=c₁e^(-ρt)cos(ω₁t-α₁) . Determine c₁, ω₁, ρ and α₁.

c₁=?
ω₁=?

ρ=?

α₁=?

Graph the function x(t) together with the "amplitude envelope" curves x=-c₁e^(-ρt) and x=c₁e^(-ρt).

Now assume the mass is set in motion with the same initial position and velocity, but with the dashpot disconnected ( so c=0). Solve the resulting differential equation to find the position function u(t).
In this case the position function u(t) can be written as u(t)=c₀cos(ω₀t-α₀). Determine c₀, ω₀,and α₀.

c₀=?
ω₀=?

α₀=?

Expert Solution

genius_generous answered 2 years ago

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