8.4 OLD EXAM PROBLEMS (from MEC 702)

1. When a force ‘F’ is applied to the spring-mass-damper system below, the result is a motion ‘x’. If the spring-damper pair should have a static spring coefficient of 500 KN/m, but at 100Hz we want an isolation of 99.9%. What is the required damper value. Clearly state any assumptions made.

2. The applied force ‘F’ is the input to the system, and the output is the displacement ‘x’.

3. Given the transfer function below,

a) draw the straight line approximation of the bode and phase shift plots.

b) determine the steady state output if the input is x(s) = 20 cos(9t+.3)

4. Given the following time response to a step input of F=5N for t >= 0, find the transfer function x/F.

1. Given the transfer function below, find the isolation at 2Hz. (25%)

2. Describe how an active vibration control system might work. (5%)

3. A 160lb sign is to be mounted onto the side of a building. One significant problem is that the sign vibrates at about 100 radians per second. Therefore isolators will be used between the sign and the side of the building. Using the specifications sheet that was supplied by a local sales office, select a suitable isolator. (10%)

4. Two identical sources have a combined amplitude (Lp) of 104dB. What would be the value of the root mean square pressure for just one of the sources? (5%)

5. The sound spectrum below is known to exist for an industrial machine. Keeping in mind the proximity of some of the peaks, what bandwidth would our sound instrumentation require to tell them apart? (5%)

6. There is a small room that contains an average 100 hp diesel engine turning at 7200 rpm. The room is 2.5m by 2.5m and has a ceiling height of 2m. The walls and ceiling of the room are coverered by a sound absorbtion coating (with a coefficient of 0.92). There are two 50cm by 30cm heavy plate glass windows in the walls for safety, and the floor is unpainted concrete. (50%)

a) determine the sound power level of the sound source (in dB).

b) assuming uniform directivity, what would be the direct sound pressure level (in dB) would we hear standing 0.5m and 2m away?

c) what is the reverberant sound pressure level (in dB) we would hear standing 0.5 and 2m away?

d) assuming the noise from the engine is relatively uniform in intensity from 200 Hz to 4 KHz, how far apart would two people in the room have to stand to hear each other shouting based on reverberant sound only?

e) what would the longest period of time a worker could be in that room each day based on reverberant sound only?

1. Given the transfer function below,

a) draw the straight line approximation of the bode and phase shift plots.(8%)

b) determine the steady state output if the input is x(s) = 20 cos(100t+.3). (4%)

2. Given the following time response to a step input of F=5N for t >= 0, find the transfer function x/F. (6%)

3. A spring damper system supports a mass of 34N. If it has a spring constant of 20.6N/cm, what is the systems natural frequency? (4%)

4. A large machine weighs 1000kg and vibrates at 20Hz, design an inertial damper. (4%)

5. If we had two sound sources at 120 Hz and 142 Hz that we wanted to measure separately, what would be the bandwidth of the analyzer? (4%)

6. A design is specified so that it should have a maximum preferred noise criteria value of 35. When tested, the sound values measured at half octaves from 63Hz are, (4%)

41dB, 43dB, 46dB, 51dB, 48dB, 48dB, 35dB, 33dB

7. Expecting an increase in business, the Boris and Natasha Detective Agency has hired you to build a soundproof wall to divide their cork lined interrogation room. The dimensions and location of the new rooms are shown below. The loudest voice expected in either room will be 80dB, and a listener can hear voices at pressure levels above 20dB.Will a 2x4” stud wall with gypsum on both sides prevent a listener from hearing another interrogation? (15%)

8. You think that a bend in a hallway of your house reduces noise levels. This “plenum” has the dimensions below. Determine the Transmission Loss for 500 Hz. (10%)

9. The following data was recorded for a non-isotropic source. What would be the directivity factor (Q) in direction θ = 60° (use appropriate approximation for calculation of the average value). (6%)

θ(deg): 0, 60, 120, 180, 240, 300

Lp(dB): 77, 71, 69, 70, 69, 73

10. Given the transfer function below, find the isolation at 2Hz. (15%)

11. There is a small room that contains an average 100 hp diesel engine turning at 7200 rpm. The room is 2.5m by 2.5m and has a ceiling height of 2m. The walls and ceiling of the room are covered by a sound absorption coating (with a coefficient of 0.92). There are two 50cm by 30cm heavy plate glass windows in the walls for safety, and the floor is unpainted concrete. (20%)

a) determine the sound power level of the sound source (in dB).

b) assuming uniform directivity, what would be the direct sound pressure level (in dB) would we hear standing 0.5m and 2m away?

c) what is the reverberant sound pressure level (in dB) we would hear standing 0.5 and 2m away?

d) assuming the noise from the engine is relatively uniform in intensity from 200 Hz to 4 KHz, how far apart would two people in the room have to stand to hear each other shouting based on reverberant sound only?

e) what would the longest period of time a worker could be in that room each day based on reverberant sound only?