7.1

Given the following system, determine the solution of the homogenous equation (which is normally called either the complementary or transient solution) for the given initial conditions:

7.2

Given the following equation for a mass spring damper system

where we assume

1. the system is massless

2. the spring has an initial displacement of Y = 10 in.

3. the spring constant equals 5 lb/in.

4. the damping coefficient equals 0.1 (lb-s/in.).

Given the initial condition, X(0) = 2, find

1. the complementary or transient solution

2. the particular or steady state solution

3. the general or total solution

7.3

Using the baseline system of Problem 7.2, find the general or total solution if the forcing function is not a constant (that is, step) but of the form

with ? = 2 rad/s.

7.4

For Problem 7.2 (with the step input) find

1. time constant

2. time for the system to reach 98.2% of its final value

7.5

For the following second-order system and initial conditions, find the transient solution:

7.6

Given M = 2, C = 12, K = 50, Y = 2

1. Write out the equation for a mass spring damper system where the initial displacement is 2.

2. Find the transient or complementary solution.

3. Find the steady state or particular solution.

4. Find the total or general solution.

5. Evaluate the two unknown coefficients in the general solution given the following initial conditions:

7.7

Write out the general solution to Problem 7.6, Part (5), in the phase angle form.

7.8

Sketch the time response to...