Problem P

The differential equation governing the motion of a ball attached to a spring is given above. Use that equation to answer the following questions.

1. Is this harmonic motion simple, under-damped, critically-damped, or over-damped?
2. Write the general solution for position as a function of time, x(t), for this equation, using symbols.
3. What is the angular frequency of this motion?
4. What is the period of this motion?
5. The initial conditions are measured to be
   • x(0) = -2.5 meters
   • v_x(0) = 1.0 meter/s
   Write the particular solution for position as a function of time, x(t), which satisfies these initial conditions. Include units for all numerical values.
6. Sketch a graph showing the position as a function of time over the range 0 < t < 10 seconds.