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improper valve selection and sizing, improper flow measurement, sounds like the problem is at the management level.

Improper valve sizing, inappropriate flow meter, sound like the problem is higher up.

the inertial response always lags in single mode systems. So the shock force is applied at t=0, with unspecified rise time (rate of rise), but fast enough to excite higher order modes, before the force is removed.

How often do you flush the system?

Your materials of construction, ppm of Cl-, and service temperature. What is being done with the treated water, downstream.

You'll need to consider what your customer is trying to achieve. Sounds like you are using heat mats to provide heat tracing of your piping or duct work. At issue: thermowells are intrusive pipe fittings used to measure the process fluid temperature, whereas if you are trying to control the...

You need to consult your projects engineering guidelines or the various engineering Standards PTC-19.3TW or the API standards.

You'll have to explain what your customer means by "heating elements," and the purpose of the measurements. You may need access to the piping layout drawings to sort out your question.

You'll need to review you process flow diagram and the material-energy balance calculations for your process. It is a bit more complicated than a spreadsheet calculation. Sulfur In = Sulfur Out The problem is that both sides of the equation consist of several components and chemical form.

Clarence Zener, formulated a quantum mechanical model of elastic damping in 1940, and offered experimental evidence to support his calculations. Damping has to do with the nanometer scale imperfections in the material, that are affected under stress-strain conditions.

You'll need to purchase your own copy.

https://www.acoustics.asn.au/conference_proceedings/AASNZ2016/papers/p108.pdf

Ref OP you have described a gas line that is improperly designed. There is no quick fix.

You'll need to check where your steam traps are located along your line, to insure proper heating the entire length of the line, as well as temperature monitoring.

The density of CH4 os drastically smaller than CO2, and quickly moves into the upper atmosphere, where solar ionization is much more intense. As a consequence it is converted to CO2 and sinks closer to the earths surface.

Don't forget flare stacks are tall and dangerous for several reasons. Failure to use one, invites a disaster, and crininal punishment.

Free-Free B.C. for slender beam: fi=Lambda^2(EI/m)^0.5/(2 pi L^2) Lambda(1)=4.7304074, etc. Courtesy "Formulas for Natural Frequency and Mode Shapes." No meaningful assumptions, other than gently taping the beam while in free-fall.

OP: "Not sure a backpressure regulator will work since the upstream pressure is pretty constant" However, as you have explained the pressure regulator cannot control the pressure. You can set the regulator but without downstream containment or partially restricted flow, it cannot maintain...

If the OP is close to an Airport or a military base, especially in the flight path, there might be a knock on the door.

Pressure regulators only work with resticted or zero flow downstream. If your sripper operates at some pressure, its gas / vapor discharge requires a back pressure regulator compatable with the fluids involved.