amplitude and phase shift original deNiUvLCgtLS1JI0BARzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiRJIkRHRikiIiM2I0kieEdGLDYjSSJ0R0YsIiIiLS1GLkYwRjIiIiUtRjFGMiIiJiwkLUkkY29zR0YpNiMsJEYzIiIkIiM1Ly1GMTYjIiIhRkQvLUY2RkNGRA==LUknZHNvbHZlRzYiNiQ8JS8sKC0tLUkjQEBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2JEkiREdGLSIiIzYjSSJ4R0YkNiNJInRHRiQiIiItLUYxRjNGNSIiJS1GNEY1IiImLCQtSSRjb3NHRi02IywkRjYiIiQiIzUvLUY0NiMiIiFGRy8tRjlGRkZHPCNGOw==E&P3 5.6.11 phase shifted cosine form of steady state solution: 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We compute in degrees and the acute reference angle LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEnYXJjdGFuRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUkjbW5HRiQ2JFEiM0YnRjJGMkYyRjI=, the actual lag angle in the second quadrant on the unit circle LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEnJiM5NjA7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RKCZtaW51cztGJ0YyLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EsMC4yMjIyMjIyZW1GJy8lJ3JzcGFjZUdGSS1GLDYlUSdhcmN0YW5GJ0YvRjItSShtZmVuY2VkR0YkNiQtRiM2JC1JI21uR0YkNiRRIjNGJ0YyRjJGMkYy, and the fraction of a cycle that it represents:QyQtSSZldmFsZkclKnByb3RlY3RlZEc2IywkKigtSSdhcmN0YW5HNiI2IyIiJCIiIkkoZGVncmVlc0dGK0YuSSNQaUdGJSEiIiIkIT1GLg==QyQvSSxwaGFzZV9zaGlmdEc2IiwmSShkZWdyZWVzR0YlIiQhPUkiJUdGJSEiIiIiIg==KigtSSRyaHNHJSpwcm90ZWN0ZWRHNiNJIiVHNiIiIiJJJ2N5Y2xlc0dGKEYpLUkiL0c2JEYlSShfc3lzbGliR0YoNiMsJEkoZGVncmVlc0dGKCIkZyRGKQ==The amplitude is just 1/4 times the square root of 1 plus LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1cEdGJDYlLUkjbW5HRiQ2JFEiM0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GIzYlLUYvNiRRIjJGJ0YyLyUnaXRhbGljR1EldHJ1ZUYnL0YzUSdpdGFsaWNGJy8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRidGMg==:PkkqYW1wbGl0dWRlRzYiLCQtSSVzcXJ0R0YkNiMkIiM1IiIhIyIiIiIiJQ==confirmation of agreementMaple knows the difference is zero but we have to prevent the trig functions of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW5HRiQ2JFEiM0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RIn5GJ0YvLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y4LyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRkctSSNtaUdGJDYlUSJ0RicvJSdpdGFsaWNHUSV0cnVlRicvRjBRJ2l0YWxpY0YnRi8= from expanding (triple angle identities!) by replacing it by a single string "phase" to see this:QyQvLCYtSSRjb3NHNiI2IywkSSJ0R0YnIiIkIyEiIiIiJS1JIipHJSpwcm90ZWN0ZWRHNiQsJC1JJHNpbkdGJ0YoRisjIiIiRi5GNyomLUklc3FydEc2JEYxSShfc3lzbGliR0YnNiMtRjA2JCIjNUY2RjctRiY2Iy1JIitHRjE2JEYpLCZJI1BpR0YxRi0tSSdhcmN0YW5HRjs2I0YrRjdGN0Y3LUkpc2ltcGxpZnlHNiI2Iy1JJ2V4cGFuZEclKnByb3RlY3RlZEc2IywoLUkkY29zR0YkNiNJJnBoYXNlR0YkIyEiIiIiJS1JIipHRig2JCwkLUkkc2luR0YkRi0iIiQjIiIiRjFGOiomLUklc3FydEc2JEYoSShfc3lzbGliR0YkNiMiIzVGOi1GLDYjLUkiK0dGKDYkRi4sJkkjUGlHRihGMC1JJ2FyY3RhbkdGPjYjRjhGOkY6Ri8=This plot shows the phase difference relative to the standard cosine graph at unit amplitude, where you see the 0.3 cycle shift to the right and the 0.8 amplitude clearly:LUklcGxvdEc2IjYlNyYtSSRjb3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2IywkSSJ0R0YkIiIkLCZGJyMhIiIiIiUtSSIqR0YqNiQsJC1JJHNpbkdGKUYsRi8jIiIiRjNGO0kqYW1wbGl0dWRlR0YkLCRGPEYyL0YuOyIiISwkSSNQaUdGKiIiIy9JJmNvbG9yR0YkNyZJJmdyZWVuR0YkSSRyZWRHRiRJJWdyYXlHRiRGSQ==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=The response curve (red) lags behind the driving cosine (green) by 18 degrees past 1/4 cycle (not so easy to interpret perhaps), or 0.30 cycles (simple, 1/5 of a quarter cycle beyond a 1/4 cycle)