Suppose the position (measured in meters) of a mass on a…
Suppose the position (measured in meters) of a mass on a spring, x(t), is modeled by the ODE: . When x(t)>0 the spring is stretched, and the spring is compressed when x(t). Answer parts (a)(b)(c) a) Solve for the position of the mass x(t) b) How far does the mass get from the equilibrium position? c) Keeping the initial position at x(0) = 0, what initial velocity would you have to give in order to make the mass get exactly 10 meters away from the equilibrium position before it turns around and heads back to the equilibrium position? That is, you need to determine what x'(0) needs to be to achieve this. Hint: you first need to determine how the amplitude depends on x'(0).