{"id":2865,"date":"2024-07-20T16:36:54","date_gmt":"2024-07-20T23:36:54","guid":{"rendered":"https:\/\/gantovnik.com\/bio-tips\/?p=2865"},"modified":"2024-07-26T19:30:23","modified_gmt":"2024-07-27T02:30:23","slug":"439-relative-accelerometer-displacement-during-sine-vibration","status":"publish","type":"post","link":"https:\/\/gantovnik.com\/bio-tips\/2024\/07\/439-relative-accelerometer-displacement-during-sine-vibration\/","title":{"rendered":"#439 Relative Accelerometer Displacement During Sine Vibration"},"content":{"rendered":"

“If you want to find the secrets of the universe, think in terms of energy, frequency, and vibration.”
\n(Nikola Tesla)<\/p>\n

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import math\nimport numpy as np\nimport matplotlib.pyplot as plt\nfrom scipy.optimize import fmin\npi=math.pi\n\nf=6.0 # f, Hz\nT=1\/f #T, s\nomega=2.0*pi*f # Hz\ng=386.100 # in\/s^2\n\ndef func_a(angle,a0,phase):\n    # a0 = acceleration maginitude, g\n    # phase, deg\n    phase_rad=phase*pi\/180.0\n    a=a0*np.cos(omega*angle-phase_rad)\n    return a\n\ndef func_d(angle,d0,phase):\n    # a0 = acceleration maginitude, g\n    # phase, deg\n    d=d0*np.cos(omega*angle-phase*pi\/180.0)\n    return d\n\n\nn=200\nx=np.linspace(0.0, T, num=n)\na0_1=10.0\nphase_1=30.0\nd0_1=a0_1*g\/omega**2\nplt.plot(x,func_a(x,a0_1,phase_1),label=\"Accel 1\")\na0_2=8.0\nphase_2=25.0\nd0_2=a0_2*g\/omega**2\n\nplt.plot(x,func_a(x,a0_2,phase_2),label=\"Accel 2\")\nplt.title('Acceleration in time domain')\nplt.xlabel('Frequency, Hz')\nplt.ylabel('Acceleration, g')\nplt.legend(loc=\"lower right\")\nplt.grid()\nplt.savefig(\"ex419_1_res100.png\", dpi=100)\nplt.savefig(\"ex419_1_res200.png\", dpi=200)\nplt.show()\n\n\nplt.plot(x,func_d(x,d0_1,phase_1),label=\"Accel 1\")\nplt.plot(x,func_d(x,d0_2,phase_2),label=\"Accel 2\")\nplt.title('Displacement in time domain')\nplt.xlabel('Frequency, Hz')\nplt.ylabel('Displacement, in')\nplt.legend(loc=\"lower right\")\nplt.grid()\nplt.savefig(\"ex419_2_res100.png\", dpi=100)\nplt.savefig(\"ex419_2_res200.png\", dpi=200)\nplt.show()\n\nplt.plot(x,func_d(x,d0_1,phase_1),label=\"Disp 1\")\nplt.plot(x,func_d(x,d0_2,phase_2),label=\"Disp 2\")\nplt.title('Displacement in time domain')\nplt.xlabel('Frequency, Hz')\nplt.ylabel('Displacement, in')\nplt.legend(loc=\"lower right\")\n\ndef delta(x):\n    d = func_d(x,d0_1,phase_1) - func_d(x,d0_2,phase_2)\n    return d\n\nplt.plot(x,delta(x),label=\"Relative disp\")\nplt.title('Relative displacement in time domain')\nplt.xlabel('Frequency, Hz')\nplt.ylabel('Displacement, in')\n\nmax_x = fmin(lambda x: -delta(x), 0.01)\nmax_y=delta(max_x[0])\nprint(\"x_max=\",max_x[0],\"y_max=\",max_y)\nplt.scatter(max_x, max_y, color='r', zorder=1,label=\"Max diff\")\nplt.axvline(x=max_x,color='r', linestyle='--')\nplt.legend(loc=\"lower right\")\nplt.grid()\nplt.savefig(\"ex419_3_res100.png\", dpi=100)\nplt.savefig(\"ex419_3_res200.png\", dpi=200)\nplt.show()<\/pre>\n","protected":false},"excerpt":{"rendered":"
“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): # a0 = acceleration maginitude, […]<\/p>\n","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":[38,2,51,112],"tags":[3,52,113],"class_list":["post-2865","post","type-post","status-publish","format-standard","hentry","category-engineering","category-python","category-strength-of-materials","category-vibration","tag-python","tag-strength-of-materials","tag-vibration"],"modified_by":"gantovnik","jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p8bH0k-Kd","jetpack_likes_enabled":true,"jetpack-related-posts":[{"id":3036,"url":"https:\/\/gantovnik.com\/bio-tips\/2024\/07\/443-vibration-double-amplitude\/","url_meta":{"origin":2865,"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 "engineering"","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":2208,"url":"https:\/\/gantovnik.com\/bio-tips\/2024\/06\/430-damped-harmonic-oscillator-using-python\/","url_meta":{"origin":2865,"position":1},"title":"#430 Damped harmonic oscillator using python","author":"gantovnik","date":"2024-06-03","format":false,"excerpt":"","rel":"","context":"In "differential equations"","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":6974,"url":"https:\/\/gantovnik.com\/bio-tips\/2025\/01\/456-approximate-harmonic-response-damping-extraction\/","url_meta":{"origin":2865,"position":2},"title":"#456 Approximate Harmonic Response & Damping Extraction","author":"gantovnik","date":"2025-01-05","format":false,"excerpt":"","rel":"","context":"In "engineering"","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\/2025\/01\/ex456_1-1.png?resize=350%2C200&ssl=1","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2025\/01\/ex456_1-1.png?resize=350%2C200&ssl=1 1x, https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2025\/01\/ex456_1-1.png?resize=525%2C300&ssl=1 1.5x, https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2025\/01\/ex456_1-1.png?resize=700%2C400&ssl=1 2x, https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2025\/01\/ex456_1-1.png?resize=1050%2C600&ssl=1 3x, https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2025\/01\/ex456_1-1.png?resize=1400%2C800&ssl=1 4x"},"classes":[]},{"id":5098,"url":"https:\/\/gantovnik.com\/bio-tips\/2024\/10\/448-torque-peaking-due-to-viscus-damper-deadband\/","url_meta":{"origin":2865,"position":3},"title":"#448 Torque Peaking Due to Viscus Damper Deadband","author":"gantovnik","date":"2024-10-19","format":false,"excerpt":"","rel":"","context":"In "vibration"","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":4043,"url":"https:\/\/gantovnik.com\/bio-tips\/2024\/09\/446-mechanical-vibrations-of-a-material-point\/","url_meta":{"origin":2865,"position":4},"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 "differential equations"","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":1558,"url":"https:\/\/gantovnik.com\/bio-tips\/2022\/09\/210-parametric-curve-in-3d-2-2-2-2-2-2-2-2-2-2-2-2-2-3-3-2-2-3-2\/","url_meta":{"origin":2865,"position":5},"title":"#301 Buckling Glossary","author":"gantovnik","date":"2022-09-13","format":false,"excerpt":"Asymmetric buckling: When the structure has asymmetric geometry it may undergo stable buckling for a positive displacement parameter and unstable buckling if this displacement parameter is negative. Bifurcation point: A point along a primary equilibrium path (or curve) intersected by a secondary path. Beyond this point, the primary equilibrium path\u2026","rel":"","context":"In "python"","block_context":{"text":"python","link":"https:\/\/gantovnik.com\/bio-tips\/category\/python\/"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]}],"_links":{"self":[{"href":"https:\/\/gantovnik.com\/bio-tips\/wp-json\/wp\/v2\/posts\/2865","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=2865"}],"version-history":[{"count":5,"href":"https:\/\/gantovnik.com\/bio-tips\/wp-json\/wp\/v2\/posts\/2865\/revisions"}],"predecessor-version":[{"id":3030,"href":"https:\/\/gantovnik.com\/bio-tips\/wp-json\/wp\/v2\/posts\/2865\/revisions\/3030"}],"wp:attachment":[{"href":"https:\/\/gantovnik.com\/bio-tips\/wp-json\/wp\/v2\/media?parent=2865"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gantovnik.com\/bio-tips\/wp-json\/wp\/v2\/categories?post=2865"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gantovnik.com\/bio-tips\/wp-json\/wp\/v2\/tags?post=2865"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}