Following the article of Analysis and Design Open Oscillatory Systems with Forced Harmonic Motion (2), the purpose of this article is to present a model for finding the characteristics of an oscillatory system with forced harmonic motion where the acceleration will be equal zero. In this case, there is an interesting point that is related to an important difference between SHM and an oscillatory system with forced harmonic motion.
If an object is oscillating under simple harmonic motion, its linear velocity will be zero at the highest and lowest points where we have maximum displacement which is named the amplitude (A).On the other hand; at the maximum level of the displacement (x = A), the acceleration has also its maximum magnitude while at the middle (x = 0), acceleration is zero due to stop at those points in order to change direction while velocity gains its maximum magnitude at the equilibrium point (x = 0). At the extreme ends (x = A), when we have the maximum force and kinetic energy, the acceleration has its maximum magnitude. Therefore, the maximum of acceleration magnitude in simple harmonic motion occurs at maximum displacement (A) and acceleration at the middle is zero when we have the displacement equal to zero just like the below diagrams:
But there is a different story about the oscillatory systems with
forced harmonic motion. In this case, at the some points where the displacement
is not zero (x = a), we have the acceleration equal to zero. Please see below
diagrams:
Now, the question is: What are the characteristics of an
oscillatory system with forced harmonic motion where we have the acceleration
equal to zero at the point of x = a?
Below model is able to answer above question:
The components of above model are as follows:
1. In right side on cells L6:M6, we have inputs
including given data
of “Fm”, and “t”.
2. In left side on cells H6:J7, we have other inputs
including lower and upper ranges for independent variables of “m”, “b” and “ω″/ω” to reach the answers for the acceleration equal to
zero which are the characteristics of driven oscillatory system. Here, there are lower and upper
ranges which are changed by click on cell A2 and also this change will again go
back by click on cell B2 (Go & Back).
3. On cells I9:I18, we have outputs
which are the characteristics for driven oscillatory system responding to the acceleration equal to zero.
You can see below clip as the example for this model:
All researchers and individual people, who are interested in having
this model, don’t hesitate to send their request to below addresses:
