Final answer:
Mechanical vibrations can be understood and solved using the principles of harmonic motion, which involve analyzing the frequency and period of oscillation. By modifying the length or density of vibrating parts, unwanted vibrations can be prevented.
Step-by-step explanation:
Mechanical vibrations can be understood and solved using the principles of harmonic motion. When an object vibrates, it undergoes repeated back-and-forth motion around an equilibrium position. To find the solutions to mechanical vibrations, we need to determine the frequency and period of the oscillation.
- The frequency of an oscillation is the number of complete cycles or vibrations it completes in one second. It is measured in hertz (Hz). To calculate the frequency, we can use the formula f = 1/T, where f is the frequency and T is the period.
- The period of an oscillation is the time it takes to complete one full cycle. It is the inverse of the frequency and is measured in seconds (s). To calculate the period, we can use the formula T = 1/f, where T is the period and f is the frequency.
By understanding the frequency and period, we can analyze and solve mechanical vibration problems, such as adjusting the length or density of a vibrating part to avoid resonance with the engine's frequency.