An object attached to a spring undergoes simple harmonic motion modeled by the differential equation m d^2x/dt^2 + 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 18 kilograms stretches the spring 0.3 meters. Use this information to find the spring constant (use g = 9.81 m/s^2 as the acceleration of gravity). K=?
The previous mass is detached from the spring and a mass of 15 kilograms is attached. This mass is displaced 0.45 meters below equilibrium and then launched with an initial velocity of -2 meters/second. Write the equation of motion in the form x(t) = c1cos(ωt) + c2sin(ωt). Do not leave unknown constants in your equation. Note: Positions below equilibrium are considered positive. x(t)=?
Rewrite the equation of motion in the form x(t) = Asin(ωt + φ). Do not leave unknown constants in your equation. x(t)=?