{"id":6974,"date":"2025-01-05T00:23:43","date_gmt":"2025-01-05T08:23:43","guid":{"rendered":"https:\/\/gantovnik.com\/bio-tips\/?p=6974"},"modified":"2025-01-06T10:16:53","modified_gmt":"2025-01-06T18:16:53","slug":"456-approximate-harmonic-response-damping-extraction","status":"publish","type":"post","link":"https:\/\/gantovnik.com\/bio-tips\/2025\/01\/456-approximate-harmonic-response-damping-extraction\/","title":{"rendered":"#456 Approximate Harmonic Response &#038; Damping Extraction"},"content":{"rendered":"<p><a href=\"https:\/\/gantovnik.com\/bio-tips\/2025\/01\/456-approximate-harmonic-response-damping-extraction\/ex456_1-2\/\" rel=\"attachment wp-att-6992\"><img data-recalc-dims=\"1\" decoding=\"async\" class=\"alignnone size-full wp-image-6992\" src=\"https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2025\/01\/ex456_1-1.png?resize=1080%2C519&#038;ssl=1\" alt=\"\" width=\"1080\" height=\"519\" srcset=\"https:\/\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2025\/01\/ex456_1-1.png 2976w, https:\/\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2025\/01\/ex456_1-1-1280x615.png 1280w, https:\/\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2025\/01\/ex456_1-1-980x471.png 980w, https:\/\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2025\/01\/ex456_1-1-480x231.png 480w\" sizes=\"(min-width: 0px) and (max-width: 480px) 480px, (min-width: 481px) and (max-width: 980px) 980px, (min-width: 981px) and (max-width: 1280px) 1280px, (min-width: 1281px) 2976px, 100vw\" \/><\/a><\/p>\n<p><a href=\"https:\/\/gantovnik.com\/bio-tips\/2025\/01\/456-approximate-harmonic-response-damping-extraction\/ex456_2\/\" rel=\"attachment wp-att-6985\"><img data-recalc-dims=\"1\" decoding=\"async\" class=\"alignnone size-full wp-image-6985\" src=\"https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2025\/01\/ex456_2.png?resize=1080%2C321&#038;ssl=1\" alt=\"\" width=\"1080\" height=\"321\" srcset=\"https:\/\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2025\/01\/ex456_2.png 2779w, https:\/\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2025\/01\/ex456_2-1280x381.png 1280w, https:\/\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2025\/01\/ex456_2-980x292.png 980w, https:\/\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2025\/01\/ex456_2-480x143.png 480w\" sizes=\"(min-width: 0px) and (max-width: 480px) 480px, (min-width: 481px) and (max-width: 980px) 980px, (min-width: 981px) and (max-width: 1280px) 1280px, (min-width: 1281px) 2779px, 100vw\" \/><\/a><\/p>\n<a href='https:\/\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2025\/01\/ex456_2024_11_24_Approximate_Harmonic_And_Analysis_Damping_Extraction.pdf' class='small-button smallblue' target=\"_blank\">Full Article pdf<\/a>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"nf_dc_page":"","_et_pb_use_builder":"","_et_pb_old_content":"","_et_gb_content_width":"","_lmt_disableupdate":"yes","_lmt_disable":"","jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[38,40,112],"tags":[319,316,113],"class_list":["post-6974","post","type-post","status-publish","format-standard","hentry","category-engineering","category-mechanics","category-vibration","tag-damping-extraction","tag-shahriar-setoodeh","tag-vibration"],"modified_by":"gantovnik","jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p8bH0k-1Ou","jetpack_likes_enabled":true,"jetpack-related-posts":[{"id":3036,"url":"https:\/\/gantovnik.com\/bio-tips\/2024\/07\/443-vibration-double-amplitude\/","url_meta":{"origin":6974,"position":0},"title":"#443 Vibration Double Amplitude","author":"gantovnik","date":"2024-07-28","format":false,"excerpt":"\"If you want to find the secrets of the universe, think in terms of energy, frequency, and vibration.\" (Nikola Tesla)","rel":"","context":"In &quot;engineering&quot;","block_context":{"text":"engineering","link":"https:\/\/gantovnik.com\/bio-tips\/category\/engineering\/"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2024\/07\/ex483_2.png?resize=350%2C200&ssl=1","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2024\/07\/ex483_2.png?resize=350%2C200&ssl=1 1x, https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2024\/07\/ex483_2.png?resize=525%2C300&ssl=1 1.5x, https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2024\/07\/ex483_2.png?resize=700%2C400&ssl=1 2x"},"classes":[]},{"id":5098,"url":"https:\/\/gantovnik.com\/bio-tips\/2024\/10\/448-torque-peaking-due-to-viscus-damper-deadband\/","url_meta":{"origin":6974,"position":1},"title":"#448 Torque Peaking Due to Viscus Damper Deadband","author":"gantovnik","date":"2024-10-19","format":false,"excerpt":"","rel":"","context":"In &quot;vibration&quot;","block_context":{"text":"vibration","link":"https:\/\/gantovnik.com\/bio-tips\/category\/vibration\/"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2024\/10\/ex448_a.png?resize=350%2C200&ssl=1","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2024\/10\/ex448_a.png?resize=350%2C200&ssl=1 1x, https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2024\/10\/ex448_a.png?resize=525%2C300&ssl=1 1.5x, https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2024\/10\/ex448_a.png?resize=700%2C400&ssl=1 2x, https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2024\/10\/ex448_a.png?resize=1050%2C600&ssl=1 3x"},"classes":[]},{"id":2865,"url":"https:\/\/gantovnik.com\/bio-tips\/2024\/07\/439-relative-accelerometer-displacement-during-sine-vibration\/","url_meta":{"origin":6974,"position":2},"title":"#439 Relative Accelerometer Displacement During Sine Vibration","author":"gantovnik","date":"2024-07-20","format":false,"excerpt":"\"If you want to find the secrets of the universe, think in terms of energy, frequency, and vibration.\" (Nikola Tesla) import math import numpy as np import matplotlib.pyplot as plt from scipy.optimize import fmin pi=math.pi f=6.0 # f, Hz T=1\/f #T, s omega=2.0*pi*f # Hz g=386.100 # in\/s^2 def func_a(angle,a0,phase):\u2026","rel":"","context":"In &quot;engineering&quot;","block_context":{"text":"engineering","link":"https:\/\/gantovnik.com\/bio-tips\/category\/engineering\/"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2024\/07\/ex439_abstract.png?resize=350%2C200&ssl=1","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2024\/07\/ex439_abstract.png?resize=350%2C200&ssl=1 1x, https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2024\/07\/ex439_abstract.png?resize=525%2C300&ssl=1 1.5x, https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2024\/07\/ex439_abstract.png?resize=700%2C400&ssl=1 2x"},"classes":[]},{"id":4043,"url":"https:\/\/gantovnik.com\/bio-tips\/2024\/09\/446-mechanical-vibrations-of-a-material-point\/","url_meta":{"origin":6974,"position":3},"title":"#446 Mechanical vibrations of a material point","author":"gantovnik","date":"2024-09-01","format":false,"excerpt":"import numpy as np import matplotlib.pyplot as plt from scipy.integrate import odeint import math def y(t): y=np.exp(-4*t) * (1 - np.cos(t) + (np.cos(1.0)-1)\/np.sin(1.0)*np.sin(t)) return y plt.rcParams[\"figure.figsize\"] = [5.50, 5.50] plt.rcParams[\"figure.autolayout\"] = True t = np.linspace(0, 1, 100) plt.plot(t, y(t)) plt.grid() plt.xlabel('t') plt.ylabel('y(t)') plt.savefig(\"ex446.png\", dpi=100) plt.show()","rel":"","context":"In &quot;differential equations&quot;","block_context":{"text":"differential equations","link":"https:\/\/gantovnik.com\/bio-tips\/category\/differential-equations\/"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2024\/09\/ex446.png?resize=350%2C200&ssl=1","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2024\/09\/ex446.png?resize=350%2C200&ssl=1 1x, https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2024\/09\/ex446.png?resize=525%2C300&ssl=1 1.5x"},"classes":[]},{"id":2208,"url":"https:\/\/gantovnik.com\/bio-tips\/2024\/06\/430-damped-harmonic-oscillator-using-python\/","url_meta":{"origin":6974,"position":4},"title":"#430 Damped harmonic oscillator using python","author":"gantovnik","date":"2024-06-03","format":false,"excerpt":"","rel":"","context":"In &quot;differential equations&quot;","block_context":{"text":"differential equations","link":"https:\/\/gantovnik.com\/bio-tips\/category\/differential-equations\/"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2024\/06\/ex430.png?resize=350%2C200&ssl=1","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2024\/06\/ex430.png?resize=350%2C200&ssl=1 1x, https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2024\/06\/ex430.png?resize=525%2C300&ssl=1 1.5x"},"classes":[]},{"id":374,"url":"https:\/\/gantovnik.com\/bio-tips\/2019\/01\/tkinter-pack-geometry-manager\/","url_meta":{"origin":6974,"position":5},"title":"#53 Tkinter pack geometry manager","author":"gantovnik","date":"2019-01-30","format":false,"excerpt":"","rel":"","context":"In &quot;python&quot;","block_context":{"text":"python","link":"https:\/\/gantovnik.com\/bio-tips\/category\/python\/"},"img":{"alt_text":"example63","src":"https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2019\/01\/example63.png?resize=350%2C200&ssl=1","width":350,"height":200},"classes":[]}],"_links":{"self":[{"href":"https:\/\/gantovnik.com\/bio-tips\/wp-json\/wp\/v2\/posts\/6974","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gantovnik.com\/bio-tips\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gantovnik.com\/bio-tips\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gantovnik.com\/bio-tips\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gantovnik.com\/bio-tips\/wp-json\/wp\/v2\/comments?post=6974"}],"version-history":[{"count":5,"href":"https:\/\/gantovnik.com\/bio-tips\/wp-json\/wp\/v2\/posts\/6974\/revisions"}],"predecessor-version":[{"id":6998,"href":"https:\/\/gantovnik.com\/bio-tips\/wp-json\/wp\/v2\/posts\/6974\/revisions\/6998"}],"wp:attachment":[{"href":"https:\/\/gantovnik.com\/bio-tips\/wp-json\/wp\/v2\/media?parent=6974"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gantovnik.com\/bio-tips\/wp-json\/wp\/v2\/categories?post=6974"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gantovnik.com\/bio-tips\/wp-json\/wp\/v2\/tags?post=6974"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}