{"id":4636,"date":"2021-01-19T00:11:51","date_gmt":"2021-01-18T23:11:51","guid":{"rendered":"https:\/\/www.nickzom.org\/blog\/?p=4636"},"modified":"2024-04-23T16:00:00","modified_gmt":"2024-04-23T15:00:00","slug":"how-to-calculate-and-solve-for-transfer-function-sensitivity-second-order-instruments-dynamic-characteristics-of-instruments","status":"publish","type":"post","link":"https:\/\/www.nickzom.org\/blog\/2021\/01\/19\/how-to-calculate-and-solve-for-transfer-function-sensitivity-second-order-instruments-dynamic-characteristics-of-instruments\/","title":{"rendered":"How to Calculate and Solve for Transfer Function (Sensitivity) | Second Order Instruments | Dynamic Characteristics of Instruments"},"content":{"rendered":"

\"\"<\/p>\n

The image above represents transfer function (sensitivity). To calculate transfer function (sensitivity) | Second Order Instrument, five essential parameters are needed and these parameters are Static Sensitivity (k), Dumping Ratio (\u03b5), Undefined Natural Frequency (\u03c9o<\/sub>), Differentiation Value (d<\/sup>\u00a0\/\u00a0dt<\/sub>) (D)\u00a0<\/strong>and\u00a0Differentiation Value (d2<\/sup>\u00a0\/\u00a0dt2<\/sup><\/sub>) (D2<\/sup>).<\/strong><\/p>\n

The formula for calculating transfer function (sensitivity):<\/strong><\/h3>\n

c =\u00a0k<\/sup>\u00a0\/\u00a01 +\u00a02\u03b5D<\/sup>\u00a0\/\u00a0\u03c9o\u00a0+\u00a0D2<\/sup>\u00a0\/\u00a0\u03c9o2<\/sup><\/sub><\/p>\n

Where:<\/p>\n

c = Sensitivity
\nk = Static Sensitivity
\n\u03b5 = Dumping Ratio
\n\u03c9o<\/sub>\u00a0= Undefined Natural Frequency
\nD = Differential Value
\nD2<\/sup>\u00a0= Differential Value<\/p>\n

Let’s solve an example;
\nFind the transfer function when the static sensitivity is 8, the dumping ratio is 12, the undefined natural frequency is 10, the differential value is 7 and the differential value is 3.<\/p>\n

This implies that;<\/p>\n

k = Static Sensitivity = 8
\n\u03b5 = Dumping Ratio = 12
\n\u03c9o<\/sub> = Undefined Natural Frequency = 10
\nD = Differential Value = 7
\nD2<\/sup> = Differential Value = 3<\/p>\n

c =\u00a0k<\/sup>\u00a0\/\u00a01 +\u00a02\u03b5D<\/sup>\u00a0\/\u00a0\u03c9o\u00a0+\u00a0D2<\/sup>\u00a0\/\u00a0\u03c9o2<\/sup><\/sub>
\nThen, c = 8<\/sup>\u00a0\/\u00a01 +\u00a02 x 12 x 7<\/sup>\u00a0\/\u00a010\u00a0+\u00a03<\/sup>\u00a0\/\u00a0102<\/sup><\/sub>
\nc =\u00a08<\/sup>\u00a0\/\u00a01 +\u00a0168<\/sup>\u00a0\/\u00a010\u00a0+\u00a03<\/sup>\u00a0\/\u00a0100<\/sub>
\nc =\u00a08<\/sup>\u00a0\/\u00a01 + 16.8 + 0.03<\/sub>
\nSo, c = 8<\/sup>\u00a0\/\u00a017.830<\/sub>
\nc = 0.448<\/p>\n

Therefore, the\u00a0transfer function (sensitivity)\u00a0<\/strong>is\u00a00.448.<\/strong><\/p>\n

Read more:\u00a0How to Calculate and Solve for Time Constant | Second Order Instruments | Dynamic Characteristics of Instruments<\/a><\/p>\n

How to Calculate Transfer Function (Sensitivity) | Second Order Instruments With Nickzom Calculator<\/strong><\/h3>\n

Nickzom Calculator \u2013 The Calculator Encyclopedia<\/strong> is capable of calculating the transfer function (sensitivity) | second Order Instrument.<\/p>\n

To get the answer and workings of the transfer function (sensitivity) | second Order Instrument using the Nickzom Calculator \u2013 The Calculator Encyclopedia.\u00a0<\/strong>First, you need to obtain the app.<\/p>\n

You can get this app via any of these means:<\/p>\n

Web<\/strong>\u00a0\u2013\u00a0https:\/\/www.nickzom.org\/calculator-plus<\/a><\/p>\n

To get access to the\u00a0professional\u00a0<\/strong>version via web, you need to\u00a0register<\/strong>\u00a0and\u00a0subscribe\u00a0<\/strong>for\u00a0NGN 2,000\u00a0<\/strong>per\u00a0annum<\/strong>\u00a0to have utter access to all functionalities.
\nYou can also try the\u00a0demo\u00a0<\/strong>version via\u00a0https:\/\/www.nickzom.org\/calculator<\/a><\/p>\n

Android (Paid)<\/strong>\u00a0\u2013\u00a0https:\/\/play.google.com\/store\/apps\/details?id=org.nickzom.nickzomcalculator<\/a>
\nAndroid (Free)<\/strong>\u00a0\u2013\u00a0https:\/\/play.google.com\/store\/apps\/details?id=com.nickzom.nickzomcalculator<\/a>
\nApple (Paid)<\/strong>\u00a0\u2013\u00a0https:\/\/itunes.apple.com\/us\/app\/nickzom-calculator\/id1331162702?mt=8<\/a>
\nOnce, you have obtained the calculator encyclopedia app, proceed to the\u00a0Calculator Map,\u00a0<\/strong>then click on\u00a0Materials and Metallurgical\u00a0<\/b>under\u00a0Engineering<\/strong>.<\/strong><\/p>\n

\"\"<\/p>\n

Now, Click on\u00a0instrumentation\u00a0<\/strong>under\u00a0Materials and Metallurgical<\/strong><\/p>\n

\"\"<\/p>\n

Now, Click on\u00a0Dynamic Characteristics of Instruments\u00a0<\/strong>under\u00a0Instrumentation<\/strong><\/p>\n

\"\"<\/p>\n

Then, Click on Transfer Function (sensitivity)| Second Order Instrument <\/strong>under\u00a0Dynamic Characteristics of Instruments<\/strong><\/p>\n

\"How<\/p>\n

The screenshot below displays the page or activity to enter your values, to get the answer for the transfer function (sensitivity) | second Order Instrument according to the respective parameters which is the Static Sensitivity (k), Dumping Ratio (\u03b5), Undefined Natural Frequency (\u03c9o<\/sub>), Differentiation Value (d<\/sup>\u00a0\/\u00a0dt<\/sub>) (D)\u00a0<\/strong>and\u00a0Differentiation Value (d2<\/sup>\u00a0\/\u00a0dt2<\/sup><\/sub>) (D2<\/sup>).<\/strong><\/p>\n

\"How<\/p>\n

Now, enter the values appropriately and accordingly for the parameters as required by the Static Sensitivity (k)<\/strong> is 8<\/strong>, Dumping Ratio (\u03b5)<\/strong> is 12<\/strong>, Undefined Natural Frequency (\u03c9o<\/sub>)<\/strong> is 10<\/strong>, Differentiation Value (d<\/sup>\u00a0\/\u00a0dt<\/sub>) (D)<\/strong> is 7 <\/strong>and Differentiation Value (d2<\/sup>\u00a0\/\u00a0dt2<\/sup><\/sub>) (D2<\/sup>)<\/strong> is 3<\/strong>.<\/p>\n

\"\"<\/p>\n

Finally, Click on Calculate<\/p>\n

\"How
\n\"\"<\/p>\n

As you can see from the screenshot above,\u00a0Nickzom Calculator<\/strong>\u2013 The Calculator Encyclopedia solves for the transfer function (sensitivity) | second Order Instrument and presents the formula, workings and steps too.<\/p>\n","protected":false},"excerpt":{"rendered":"The image above represents transfer function (sensitivity). To calculate transfer function (sensitivity) | Second Order Instrument, five essential…","protected":false},"author":5,"featured_media":14364,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_opengraph-title":"","_yoast_wpseo_opengraph-description":"","_yoast_wpseo_twitter-title":"","_yoast_wpseo_twitter-description":"","_lmt_disableupdate":"","_lmt_disable":"","_sitemap_exclude":false,"_sitemap_priority":"","_sitemap_frequency":"","_yoast_wpseo_focuskw_text_input":"","csco_display_header_overlay":false,"csco_singular_sidebar":"","csco_page_header_type":"","footnotes":"","_members_access_role":[],"_members_access_error":""},"categories":[47],"tags":[1353,1348,60,1329,543,1350,1354],"class_list":["post-4636","post","type-post","status-publish","format-standard","has-post-thumbnail","category-engineering","tag-dumping-ratio","tag-dynamic-characteristics-of-instruments","tag-engineering","tag-instrumentation","tag-materials-and-metallurgical","tag-time-constant","tag-undefined-natural-frequency","cs-entry"],"yoast_head":"\nHow 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