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An object attached to a spring undergoes simple harmonic motion modeled by the differential equation d²x + kx = 0 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 6 kilograms stretches the spring 0.6 meters. dt² Use this information to find the spring constant. (Use g = 9.8 meters/second²) m. k = The previous mass is detached from the spring and a mass of 8 kilograms is attached. This mass is displaced 0.15 meters above equilibrium 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. x(t) = Rewrite the equation of motion in the form x(t) = A sin(wt + o), where 0 ≤ < 2π. Do not leave unknown constants in your equation. x(t) =

An object attached to a spring undergoes simple harmonic motion modeled by the differential equation d²x + kx = 0 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 6 kilograms stretches the spring 0.6 meters. dt² Use this information to find the spring constant. (Use g = 9.8 meters/second²) m. k = The previous mass is detached from the spring and a mass of 8 kilograms is attached. This mass is displaced 0.15 meters above equilibrium 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. x(t) = Rewrite the equation of motion in the form x(t) = A sin(wt + o), where 0 ≤ < 2π. Do not leave unknown constants in your equation. x(t) =

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An object attached to a spring undergoes simple harmonic motion modeled by the differential equation d²x + kx = 0 where x (t) is the displacement of the mass (relative to equilibrium) at time t, m is the dt² mass of the object, and k is the spring constant. A mass of 6 kilograms stretches the spring 0.6 meters. Use this information to find the spring constant. (Use g = 9.8 meters/second²) m k = The previous mass is detached from the spring and a mass of 8 kilograms is attached. This mass is displaced 0.15 meters above equilibrium 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. x(t) Rewrite the equation of motion in the form ä(t) = A sin(wt + p), where 0 ≤ ☀ < 2π. Do not leave unknown constants in your equation. x(t) =
Transcribed Image Text:An object attached to a spring undergoes simple harmonic motion modeled by the differential equation d²x + kx = 0 where x (t) is the displacement of the mass (relative to equilibrium) at time t, m is the dt² mass of the object, and k is the spring constant. A mass of 6 kilograms stretches the spring 0.6 meters. Use this information to find the spring constant. (Use g = 9.8 meters/second²) m k = The previous mass is detached from the spring and a mass of 8 kilograms is attached. This mass is displaced 0.15 meters above equilibrium 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. x(t) Rewrite the equation of motion in the form ä(t) = A sin(wt + p), where 0 ≤ ☀ < 2π. Do not leave unknown constants in your equation. x(t) =
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