Tony Spark 194 Questions 0 Answers 0 Best Answers 1k Points View Profile Tony SparkEnlightened Asked: April 25, 20202020-04-25T15:42:05+00:00 2020-04-25T15:42:05+00:00In: Advanced math questions and answers 3.1 If the differential equation of motion of a particle of mass m is written as d’x dt dx dt the… 1 Answer Voted Oldest Recent Anonymous Added an answer on April 25, 2020 at 3:42 pm Auxiliary equation: – mD^2 + f’D = 0 (mD + f’) D = 0 D = 0, D = -f’/m complementary x(t) = c_1 + c_2 e^- (f’/ m)t P.I = 1/mD^2 + f’D (F’) = 1/D(mD + f’) F’ = 1/f’D (1 + m/f’ D) F’ = 1/f’D (1 + m/f’ D)^- 1 F’ = 1/f’D (1 + m/f’ D) F’ = 1/f’ D (1 – m/f’D +…)F’ = 1/f’D . F’ = F’/f’ t x(t) = c_1 c_2 e^- (f’/m)t + F’/f’ t dx/dy = -f’/m e^- (f’/m)t + F’/f’ x(0) = 0, dx/dt = 0 at t = 0 0 = c_1 + c_2 & 0 0 Reply Share Share Share on Facebook Share on Twitter Share on LinkedIn Share on WhatsApp Leave an answerLeave an answerCancel reply Featured image Select file Browse Answer Anonymously Save my name, email, and website in this browser for the next time I comment.

Auxiliary equation: – mD^2 + f’D = 0 (mD + f’) D = 0 D = 0, D = -f’/m complementary x(t) = c_1 + c_2 e^- (f’/ m)t P.I = 1/mD^2 + f’D (F’) = 1/D(mD + f’) F’ = 1/f’D (1 + m/f’ D) F’ = 1/f’D (1 + m/f’ D)^- 1 F’ = 1/f’D (1 + m/f’ D) F’ = 1/f’ D (1 – m/f’D +…)F’ = 1/f’D . F’ = F’/f’ t x(t) = c_1 c_2 e^- (f’/m)t + F’/f’ t dx/dy = -f’/m e^- (f’/m)t + F’/f’ x(0) = 0, dx/dt = 0 at t = 0 0 = c_1 + c_2 & 0