A 10-kg mass attached to a spring with stiffness 250(N)/(m), with negligible resistance. Initially, the string is contracted by 15cm relative to its natural length and the mass is moving outward (i.e. towards the equilibrium position) at 1(m)/(sec).
(a) Sketch a diagram, indicate the variables and units and state differential equation and the intial conditions for x(t), the position of the mass as a function of time.
(b) Determine an explicit formula for x(t) and the amplitude of the resulting oscillations. Include the appropriate units.
(c) Use the formula in part b to find the earliest positive time when the direction of motion reverses from outward to inward (equivalently, the string is stretched as much as possible).
1. A 10-kg mass attached to a spring with stiffness 250 N/m,with negligible resistance. Initially the string is contracted by 15 cm relative to its natural length and the mass is moving outward (i.e.towards the equilibrium position at l m/sec a) Sketch a diagram, indicate the variables and units and state differential equation and the intial conditions for x(t), the position of the mass as a function of time. (b) Determine an explicit formula for xt and the amplitude of the resulting oscillations Include the appropriate units. c Use the formula in part b to find the earliest positive time when the direction of mo tion reverses from outward to inward (equivalently, the string is stretched as much as possible).