An object attached to a spring undergoes simple harmonic motion modeled by the differential equation k = m N/m d²x dt² 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 5 kilograms stretches the spring 0.05 meters. Use this information to find the spring constant. (Use g = 9.8 m/s²) + kx = 0 The previous mass is detached from the spring and a mass of 20 kilograms is attached. This mass is displaced 0.3 meters above equilibrium (above is positive and below is negative) and then launched with an initial velocity of 1 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. x(t) = 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 - π and T. x(t) =
An object attached to a spring undergoes simple harmonic motion modeled by the differential equation k = m N/m d²x dt² 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 5 kilograms stretches the spring 0.05 meters. Use this information to find the spring constant. (Use g = 9.8 m/s²) + kx = 0 The previous mass is detached from the spring and a mass of 20 kilograms is attached. This mass is displaced 0.3 meters above equilibrium (above is positive and below is negative) and then launched with an initial velocity of 1 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. x(t) = 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 - π 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
=
where x (t) is the displacement of the mass (relative to equilibrium) at timet, m is the
mass of the object, and k is the spring constant. A mass of 5 kilograms stretches the
spring 0.05 meters.
x (t)
Use this information to find the spring constant. (Use g
=
m
=
x (t)
d² x
dt²
N/m
+ kx
=
=
0
The previous mass is detached from the spring and a mass of 20 kilograms is attached.
This mass is displaced 0.3 meters above equilibrium (above is positive and below is
negative) and then launched with an initial velocity of 1 meters/second. Write the
equation of motion in the form ä(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 (t) = A cos(ßt p). Do not leave
unknown constants in your equation. Leave & as an angle between – í and í.
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