Question: The differential equation d 2 y / d t 2 + ( k / m ) y = 0 describes the motion of a body

The differential equation

d2y/dt2+(k/m)y=0

describes the motion of a body of mass suspended from a spring in a frictionless medium when the spring's spring constant is .

a) A 5 object is attached to a spring with a spring constant of 20 /². Give the expression for the position of the body as a function of time if initially the spring was stretched 0.5 [ (0)=0.5] beyond the stretch caused by the body and then released with a speed of 2 / ['(0)=2]. The differential equation

d2y/dt2+(a/m)dy/dt+(k/m)y=0

describes the motion of a body of mass suspended from a spring subject to a damping force (or friction) proportional to the body's speed of motion when the spring's spring constant is .

b) Answer the previous question if the body's motion is damped and the constant is equal to 20 /².

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