- #1

Gh. Soleimani

- 44

- 1

**A Case of Mechanical Waves**

**Case**

*: Is There Any Mechanical Oscillatory System Where Maximum Velocity of Resonance Will Increase More Than Speed of the Light?”*Consider a child, who is playing with a swing. During the period of the time, he learns to apply the optimum force to the swing in order to minimize efforts and maximize the amplitude of the swing. How? The answer is that driving force should be applied periodically and should be timed to coincide closely with the natural motion of the swing

**In other words, a driven oscillator responds most strongly when driven by a periodically varying force, the frequency of which is closely matched to the frequency with which the system would freely oscillate if left to it. This frequency is called the natural frequencyof the oscillator.**

*.*Assume we are designing an open system which has the damped harmonic motion and are also forced by external oscillatory forces under harmonic motion. The parameters of designing are as follows:

Fm = External force (N)

k = Restoring constant of system (N/m)

m = mass of system (kg)

b = Damped force constant of system (kg/s)

ω'' = Angular velocity of external force (rad/s)

A = Amplitude (m)

ω = Natural angular velocity (rad/s)

We are willing to know if there is any mechanical system with FHM in which maximum velocity of this system will go up more than 3E+8 m/s. What is the range for parameters of designing?

I found 17 types of the parameters where maximum velocity of our system is equal to 1E+9 m/s > c = 3E+8 m/s. It means that we can have 17 types of design for our system to reach maximum velocity more than speed of the light. All parameters for designing have been arranged into attached Table.

As we can see, the most crucial thing is that our system will reach to maximum velocity more than speed of the light, if external oscillatory force goes up more than 1KN and damped force constant decrease less than 1E-6 kg/s. In fact, the boundary conditions are:

**Fm ≥ 1KN and b ≤ 1E-6 kg/s**

**Case questions:**

- Is there really above system in the nature?
- If your answer is positive. Have you any real examples?