Chapter 1: One degree of freedom

1. Undamped vibration of a spring/mass system without damping.

2. Damped vibration of a spring/mass system with viscous damping.

3. Critically damped vibration of a spring/mass system with viscous damping.

4. Over-damped vibration of a spring/mass system with viscous damping.

5. Sinusoidal forced vibration of a one degree of freedom system.

6. Forced Response of a one degree of freedom system.

7. Construction of the response locus of damped system.

8. Out-of-balance forced vibration of a one degree of freedom system.

9. Out-of-balance forced vibration with a constant angular acceleration up to top speed.

10. Out-of-balance response of a one degree of freedom system.

11. Sinusoidal abutment vibration of a one degree of freedom system.

12. Forced abutment response of a one degree of freedom system.

13. The connection between rotating vectors, sinusoidal motion and phase.


Chapter 2: Two degree of freedom

1. Natural frequencies and mode shapes of a two degree of freedom system

2. Transient vibration of a two degree of freedom system without damping

3. Modal contributions to the transient vibration of a two degree of freedom system

4. Forced responses of a two degree of freedom system and the modal components

5. Transient vibration of a damped two degree of freedom system

6. Sinusoidal abutment vibration of a two degree of freedom system.

7. Magnitude and phase of the forced abutment response of a two degree of freedom system.

8. Sinusoidal forced vibration of a two degree of freedom system.

9. Forced Response of a two degree of freedom system.

10. Abutment response with a detuner.

11. Start up transients for abutment excitation with a detuner.

12. Forced response with a detuner.

13. Start up transients for forced excitation with a detuner.

14. Forced response with an optimised vibration absorber.


Chapter 3: Beam

1. Natural frequencies and mode shapes of a beam on two springs.

2. Transient vibration of a beam on two springs without damping.

3. Modal contributions to the transient vibration of a beam on two springs.

4. Forced response of a beam on two springs.

5. Magnitude of the forced response of a beam on two springs without damping.

6. Transient vibration of a beam on two springs with damping.

7. Magnitude of the forced response of a beam on two springs damping.


Chapter 4: Methods

1. Natural frequencies predicted from an assumed mode shape.


Chapter 5: Multi degree of freedom

1. Natural frequencies and mode shapes of a three degree of freedom system.

2. Forced responses of an undamped three degree of freedom system.

3. Forced responses of an undamped three degree of freedom system with an animation at a selected frequency.

4: Forced responses of an damped three degree of freedom system.

5. Forced responses of an damped three degree of freedom system with an animation at a selected frequency.

6. Natural frequencies and mode shapes of a five degree of freedom system.

7. Forced responses of an undamped five degree of freedom system.

8. Forced response of an undamped five degree of freedom system with an animation at a selected frequency.

9. Forced response of a damped five degree of freedom system with an animation at a selected frequency.

10. Forced response of a damped system with an animation at a selected frequency.


Chapter 6: Modal Analysis

1. Transverse modes of two masses on a string in tension.

2. Forced response of two masses on a string in tension.

3. Complex eigen values of a two degree of freedom system.

4. Forced response comparison: Exact and modal.

5. Determination of Q factor from a response curve.

6. Comparison of exact response with modal analysis response.

7. Transient response of a two degree of freedom system with viscous damping.


Chapter 7: Continuous - Axial and torsional.

1. Axial modes of a free/free bar.

2. Response of a free/free bar.

3. Response of a free/free bar with an animation at a selected frequency.

4. Axial modes of a clamped/free bar.

5. Response of a clamped/free bar with an animation at a selected frequency.

6. Tip response of a free/free damped bar with an animation at a selected frequency.

7. Tip response of a free/free tapered bar with an animation at a selected frequency.

8. Torsional modes of a free/free bar.

9. Torsional modes of a clamped/free bar.


Chapter 8: Continuous - Transverse.

1. Transverse modes of a free/free bar.

2. Transverse modes of a clamped/free bar.

3. Tip response of a free/free bar.

4. Tip response of a clamped/free bar.

5. Shear and rotary inertia effects.


Chapter 9: Receptances - a systems approach.

1. Natural frequencies of clamped/free bar attached to a spring.

2. Natural frequencies of clamped/free bar attached to a mass.

3. Natural frequencies of clamped/free bar attached to a spring/mass system.

4. Natural frequencies of clamped/free bar with a second bar attached.

5. Forced response of a damped five degree-of-freedom system.

6. Forced response of a damped system with an animation at a selected frequency.

7. Effect of coupling stiffness on natural frequency.

8. Response of a clamped/free bar with a vibration absorber attached.

9. Optimised response of a clamped/free bar with a vibration absorber attached.

10. Response of a clamped/free bar with an absorber bar and insert.

11. Optimised response of a clamped/free bar with an absorber bar and insert.