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) =
Chapter3: Polynomial Functions
Section3.5: Mathematical Modeling And Variation
Problem 7ECP: The kinetic energy E of an object varies jointly with the object’s mass m and the square of the...
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Question
![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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2323f944-68c6-4ffb-b4bd-7709a3866c17%2F94ce12e3-dd90-4afe-9f17-ce6ce15622a9%2Fcrm1ow8_processed.png&w=3840&q=75)
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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