An object attached to a spring undergoes simple harmonic motion modeled by the differential equation = m. N/m x (t) d²x dt² + kx where x(t) is the displacement of the mass (relative to equilibrium) at time t, m is the mass of the object, and k is the spring constant. A mass of 18 kilograms stretches the spring 0.1 meters. Use this information to find the spring constant. (Use g 9.8 m/s²) - 0 The previous mass is detached from the spring and a mass of 6 kilograms is attached. This mass is displaced 0.85 meters below equilibrium (above is positive and below is negative) and then launched with an initial velocity of 2 meters/second. Write the equation of motion in the form x (t) = C₁ cos(wt) + C₂ sin(wt). Do not leave unknown constants in your equation. = Rewrite the equation of motion in the form (t) A cos(Bt - 6). Do not leave unknown constants in your equation. Leave as an angle between - and T. x(t) =
An object attached to a spring undergoes simple harmonic motion modeled by the differential equation = m. N/m x (t) d²x dt² + kx where x(t) is the displacement of the mass (relative to equilibrium) at time t, m is the mass of the object, and k is the spring constant. A mass of 18 kilograms stretches the spring 0.1 meters. Use this information to find the spring constant. (Use g 9.8 m/s²) - 0 The previous mass is detached from the spring and a mass of 6 kilograms is attached. This mass is displaced 0.85 meters below equilibrium (above is positive and below is negative) and then launched with an initial velocity of 2 meters/second. Write the equation of motion in the form x (t) = C₁ cos(wt) + C₂ sin(wt). Do not leave unknown constants in your equation. = Rewrite the equation of motion in the form (t) A cos(Bt - 6). Do not leave unknown constants in your equation. Leave as an angle between - and T. x(t) =
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:An object attached to a spring undergoes simple harmonic motion modeled by the
differential equation
k =
x(t)
m
where x(t) is the displacement of the mass (relative to equilibrium) at time t, m is the
mass of the object, and k is the spring constant. A mass of 18 kilograms stretches the
spring 0.1 meters.
=
x (t)
d² x
Use this information to find the spring constant. (Use g
=
N/m
dt²
=
+ kx
=
= 0
The previous mass is detached from the spring and a mass of 6 kilograms is attached.
This mass is displaced 0.85 meters below equilibrium (above is positive and below is
negative) and then launched with an initial velocity of 2 meters/second. Write the
equation of motion in the form (t) = C₁ cos(wt) + C₂ sin(wt). Do not leave unknown
constants in your equation.
9.8 m/s²)
Rewrite the equation of motion in the form x(t) = A cos(Bt - ). Do not leave
unknown constants in your equation. Leave as an angle between - and T.
π
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