Question

5. A 2 kg mass is connected to a wall through a spring with force constant of 8 N/m. Using the Laplace transform method, calculate the time-dependent position of the mass, x(t) for t > 0, for the following cases:

   1. The mass is initially at rest, and then is hit at time zero with an impact described by f(t) = delta function.

   2. The mass is initially at rest, and then is hit at time t = 1 s with an impact described by f(t) = deltafunction(t – 1).

   3. The mass has an initial position of 1 m, and an initial velocity of zero, and there are no external forces.

   4. The mass has an initial position of zero and an initial velocity of 1 m/s, and there are no external forces.

   5. The mass has an initial position of 1 m, an initial velocity of 1 m/s and is hit by an impact described by the equation f(t) = delta function

   6. Comment on how the solution of part (e) relates to the answers of parts (a), (c) and (d).

   7. The mass has an initial position of 5 m, an initial velocity of -5 m/s and is hit by one

      impact described by the equation f(t) = 6(delta function) Hint: based on the answer to question (f), you don’t need to re-calculate all the different parts of the solution again.

Answer 1