<transcript><audio_15>second derivative you get s times that I start form of the first derivative and as u prime in 0 r u prime is 0 was given as Omega so it so you get a minus Omega from the manchu prime of 0 and then you</transcript><transcript><audio_16>can do this again you compute the Laplace transform of U prime that equals a staff Laplace transform of U minus the function value at 0 which is 0 so what you get here you have your Laplace</transcript><transcript><audio_17>transform of U prime captain mines oh my god this term becomes 0 over here so yeah we are left with an escrow types Laplace transform of U minus your Omega and it's called the Laplace transform of you just capital u of s so we get it</transcript><transcript><audio_18>esker times G of s times Omega so our second derivative becomes a square times the Laplace transform of U and some constant now what do we get further a full equation a Laplace transform it's done</transcript> second derivative you get s times that I start form of the first derivative and as u prime in 0 r u prime is 0 was given as Omega so it so you get a minus Omega from the manchu prime of 0 and then you can do this again you compute the Laplace transform of U prime that equals a staff Laplace transform of U minus the function value at 0 which is 0 so what you get here you have your Laplace transform of U prime captain mines oh my god this term becomes 0 over here so yeah we are left with an escrow types Laplace transform of U minus your Omega and it's called the Laplace transform of you just capital u of s so we get it esker times G of s times Omega so our second derivative becomes a square times the Laplace transform of U and some constant now what do we get further a full equation a Laplace transform it's done
{"source": "grass-yt-cc-by.-nmlvHEDweM|shard_10027_34|create_multimodal_data.extract_yt_and_generate_transcripts.22|shard_10027|create_multimodal_data.generate_captions.38|shard_10027|create_multimodal_data.generate_captions.38", "params": {"id": "-nmlvHEDweM", "channel_id": "UCEjpRpZSjy6mkwKqzeTeVrQ", "duration": 564, "view_count": 393, "age_limit": 0, "like_count": 1, "channel_follower_count": 4880, "license": "Creative Commons Attribution license (reuse allowed)", "uploader_id": "@MatheMagician", "yt_tar_file": "/leonardo_work/EUHPC_E03_068/audio/fixed_download/grass-yt-cc-by//shard_10027/-nmlvHEDweM.tar.gz"}}