1. A weight of 50 N is suspended from a spring of stiffness 5000 N/m and is subjected to a harmonic force of amplitude 40 N and frequency 4 Hz. Find:

(a) The extension of the spring due to suspended weight.

(b) The static displacement of the spring due to the maximum applied force.

(c) The amplitude of the forced motion of the weight.

2. A single-degree-of-freedom spring mass damper system is subjected to a harmonic force. The amplitude is found to be 25 mm at resonance and 10 mm at a frequency 0.75 times the resonant frequency. Determine the damping ratio of the system.

3. For a spring-mass-damper system where the mass is 50 kg and the spring stiffness is 5000 N/m find:

(a) the critical damping coefficient cc

(b) when c = cc/2 find (i) the damped frequency, (ii) the logarithmic decrement

4. A cylinder is 100 mm internal diameter and 200 mm outer diameter is subject to an internal pressure of 100 Mpa. Determine the maximum radial and tangential stresses on the cylinder.

5. A cylinder is 100 mm ID and 200 mm OD. If it is subject to an external pressure of 100 MPa, determine the maximum radial and tangential stresses.

6. A cylinder is 100 mm ID and 200 mm OD. If it is subject to an internal pressure of 100 MPa and an external pressure of 100 MPa. Determine the radial and tangential stresses in the cylinder.

7. A stainless steel ‘O' ring is to be designed for a high performance automobile part with an internal diameter of 100 mm and external diameter of 200 mm. The part is expected to be subjected to an internal pressure of 100 MPa due to the compressed fluid contained and an external pressure of 50 MPa due to the structural mounted components. For design purposes predict the radial and tangential stresses in the O ring at thickness intervals of 5 mm starting from the internal diameter leading up to the external. Represent the data in a graphical format to allow for design conclusions.