Old Homework 36 - portillo(gdp347 oldhomework 36...

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portillo (gdp347) – oldhomework 36 – Turner – (58185) 1 This print-out should have 6 questions. Multiple-choice questions may continue on the next column or page – fnd all choices beFore answering. 001 (part 1 oF 2) 10.0 points A 7 . 3 kg mass slides on a Frictionless surFace and is attached to two springs with spring constants 23 N / m and 64 N / m as shown in the fgure. 23 N / m 64 N / m 7 . 3 kg ±ind the Frequency oF oscillation. Correct answer: 0 . 549438 Hz. Explanation: Let : k 1 = 23 N / m , k 2 = 64 N / m , and m = 7 . 3 kg . By Hooke’s law, F = - k x = m a = m d 2 x dt 2 and d 2 x dt 2 + k m x = 0 , (1) whose integral Form has a sine Function x ( t ) = A sin( ω t + δ ) , where ω = r k m , the square root oF the coe²- cient oF x in Eq. 1. Call the displacement oF the mass x , and choose the positive direction to be to the right. Then, the Forces From the springs on the mass m are to the leFt: F 1 = - k 1 x and F 2 = - k 2 x , so that Force equilibrium is F = - k parallel x F 1 + F 2 = - k parallel x - k 1 x - k 2 x = - k parallel x k parallel = k 1 + k 2 . ω = r k m , so ω parallel = r k parallel m = r k 1 + k 2 m and the Frequency oF oscillation is f = ω parallel 2 π = r k 1 + k 2 m 2 π = r 23 N / m + 64 N / m 7 . 3 kg 2 π = 0 . 549438 Hz . 002 (part 2 oF 2) 10.0 points Now the two spring are coupled together as shown in the fgure. 23 N / m 64 N / m 7 . 3 kg ±ind the period oF oscillation. Correct answer: 4 . 12712 s.
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Old Homework 36 - portillo(gdp347 oldhomework 36...

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