SolSec 2.6 - 2-42 Problems and Solutions Section 2.6 (2.51...

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

View Full Document Right Arrow Icon
2-42 Problems and Solutions Section 2.6 (2.51 through 2.54) 2.51 Calculate damping and stiffness coefficients for the accelerometer of Figure 2.15 with moving mass of 0.04 kg such that the accelerometer is able to measure vibration between 0 and 50 Hz within 5%. ( Hint : For an accelerometer it is desirable for Y Z b 2 / ω = constant.) Solution: Use equation (2.71): Given: m = .04 kg with error < 5% .2 f = 50 Hz f = 250 Hz = 2 f π = 1570.8 rad/s Thus, k = 2 m = 98,696 N/m When r = .2, .95 < 2 2 2 ) 2 ( ) 1 ( 1 r r ζ + <1.05 (± 5% error) This becomes .8317+.1444 2 <1<1.016+.1764 2 Therefore, km c 2 7 . = = ) 04 )(. 98696 ( ) 7 (. 2 = c c = 87.956 Ns/m 2.52 The damping constant for a particular accelerometer of the type illustrated in Figure 2.15 is 50 N s/m. It is desired to design the accelerometer (i.e., choose m and k ) for a maximum error of 3% over the frequency range 0 to 75 Hz. Solution: Given .2 f = 75 Hz f = 375 Hz n = 2 f = 2356.2 rad/s. Using equation (2.84) when r = .2: .97 < 2 2 2 ) 2 ( ) 1 ( 1 r r + <1.03 (± 3% error) This becomes .8671 + .1505 2 <1<.9777+.1697 2 Therefore, 0.3622 < <0.9395 Choose ) 2 . 2356 ( 2 50 2 7 . m m c = = = m = 0.015 kg km n = 2 = 8.326
Background image of page 1

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

View Full DocumentRight Arrow Icon
Background image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 02/11/2010 for the course MECHANICAL ms316 taught by Professor Abduljaba during the Spring '09 term at Kalamazoo.

Page1 / 2

SolSec 2.6 - 2-42 Problems and Solutions Section 2.6 (2.51...

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

View Full Document Right Arrow Icon
Ask a homework question - tutors are online