An object attached to a spring undergoes simple harmonic motion modeled by the differential equation my"+ky = 0 where y(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 19 kilograms stretches the spring 0.35 meters. Use this information to find the spring constant. (Use g = -9.8 meters/second²) k = The previous mass is detached from the spring and a mass of 4 kilograms is attached. This mass is displaced 0.05 meters below equilibrium and then launched with an initial velocity of -2 meters/second. Write the equation of motion in the form y(t) = c₁ cos(wt) + c₂ sin(wt). Do not leave unknown constants in your equation. y(t) = = Rewrite the equation of motion in the form y(t) = A sin(wt + p). Do not leave unknown constants in your equation. y(t) = =
An object attached to a spring undergoes simple harmonic motion modeled by the differential equation my"+ky = 0 where y(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 19 kilograms stretches the spring 0.35 meters. Use this information to find the spring constant. (Use g = -9.8 meters/second²) k = The previous mass is detached from the spring and a mass of 4 kilograms is attached. This mass is displaced 0.05 meters below equilibrium and then launched with an initial velocity of -2 meters/second. Write the equation of motion in the form y(t) = c₁ cos(wt) + c₂ sin(wt). Do not leave unknown constants in your equation. y(t) = = Rewrite the equation of motion in the form y(t) = A sin(wt + p). Do not leave unknown constants in your equation. y(t) = =
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Transcribed Image Text:An object attached to a spring undergoes simple harmonic motion modeled by the differential equation
my"+ky = 0 where y(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 19 kilograms stretches the spring 0.35 meters.
Use this information to find the spring constant. (Use g = -9.8 meters/second²)
k
=
The previous mass is detached from the spring and a mass of 4 kilograms is attached. This mass is displaced
0.05 meters below equilibrium and then launched with an initial velocity of -2 meters/second. Write the
equation of motion in the form y(t) = c₁ cos(wt) + C₂ sin(wt). Do not leave unknown constants in your
equation.
y(t)
=
Rewrite the equation of motion in the form y(t) = A sin(wt + p). Do not leave unknown constants in your
equation.
y(t) =
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