Respuesta :
Answer:
A differential equation is [tex]4x''+3x'+98x=0[/tex].
Explanation:
Given that,
Mass = 4 kg
Stretch string = 40 cm
Additional distance = 12 cm
Damping constant = 3 N-s/m
Let xx to denote the displacement, in meters, of the mass from its equilibrium position, and give your answer in terms of x,x′,x′′ .
We need to calculate the spring constant k
The net force in y direction at equilibrium position
[tex]F_{y}=0[/tex]
[tex]mg-kx=0[/tex]
Put the value into the formula
[tex]4\times9.8-k\times40\times10^{-2}=0[/tex]
[tex]k=\dfrac{4\times9.8}{40\times10^{-2}}[/tex]
[tex]k=98\ N/m[/tex]
The initial displacement from equilibrium
[tex]x(0)=12\ cm[/tex]
The initial velocity is
[tex]v(0)=0[/tex]
We need to set up a differential equation
The net force in y direction is zero at equilibrium position .
[tex]\Sum F_{y}=0[/tex]
[tex]mx''+cx'+kx=0[/tex]
Put the value into the equation
[tex]4x''+3x'+98x=0[/tex]
Hence, A differential equation is [tex]4x''+3x'+98x=0[/tex].
