Old Homework 36

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

This preview shows pages 1–2. Sign up to view the full content.

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.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 4

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online