An object attached to a spring undergoes simple harmonic motion modeled by the differential equation md2ydt2+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 0.4 meters. Use this information to find the spring constant. (Use g=9.8 meters/second2)

k= 465.5

The previous mass is detached from the spring and a mass of 3 kilograms is attached. This mass is displaced 0.6 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 y(t)=c1cos(ωt)+c2sin(ωt). Do not leave unknown constants in your equation, and round all values to exactly 3 decimal places.

y(t)=

Rewrite the equation of motion in the form y(t)=Asin(ωt+ϕ) where ϕ is an angle between −π2 and π2. Do not leave unknown constants in your equation, and round all values to exactly 3 decimal places.

y(t)=