## 8 thoughts on “3.25”

1. Mustafa Mohammed says:

how do you get .036 for (k2*A/m)*H(r) are we supposed to divide by something else?

1. tutorpaul says:

Yes, it should be divided by $\omega_n^2$. That is shown in black above that calculation, but I failed to copy it to the lines below.

2. Trey Torno says:

I thought we were supposed to use the G(r) equation here?

1. tutorpaul says:

No, the $H(r)$ is the most appropriate transfer function to use. Notice that this system is attached to a fixed ground (via $k_1$ and $c$) and is being excited by a harmonic force (the known motion of the wall on the right transfers to the mass through the spring force).

A system necessitating the use of $G(r)$ would not be attached to a fixed ground it would only be connected to the moving plate; an arrangement of that type could be called "Base Excitiation". $J(r)$ may be appropriate for a base excitation system, if we were interested in finding the distance between the base and the mass, however in most cases we are interested in the location of the mass relative to a fixed point and we would thus use $G(r)$.

1. omar.al-ani says:

This is not the correct reason for why H(r) is the correct transfer function to use. It does not matter if the system is fixed to the ground or not.

If we added a damper to the right hand side, we would not be able to use H(r).

H(r) is used whenever the EOM is of the form y''+ay'+by=A*sin(wt).
G(r) is user whenever the EOM is of the form y''+ay'+by=A*sin(wt)+B*w*cos(wt)

1. tutorpaul says:

Omar, your answer is mechanistically correct. That is to say, once you've found the EOM your selection can be seen as correct. The reason I gave for choosing $H(r)$ can be defended without knowing the EOM; this is advantageous for approaching real-world systems because it depends specifically on the orientation of the physical system rather than the mathematical model of it.

Ultimately my method of choosing is a heuristic, and thus more failure prone than matching based on EOM (which I do advocate in other videos). Neither technique is particularly satisfying at the level of this course, because you haven't fully explored the mathematics of getting from the EOM to the transfer function (you should learn that in 364). The simple heuristic is effective, and pushes the student to get a feel for how these systems move which is why I like it.

3. ledrone says:

This problem is the same as 3.34 in the 11th edition