Lab Mass Effect Vibration

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Auto Tech 4VD3 LAB 1 Effect of Mass on Damping Characteristics – Free Vibration | Objective To understand the effects of damping on the vibration and the effects of mass on the damping characteristics Apparatus * Aluminum Frame * Vibrating Beam * Spring * Spring Attachments * Damper * Damper Attachments * 3” C- clamps (qty 3) * ADXL345 analog accelerometer development board * Micro SD card & card reader * AAA batteries (qty 2) * Weight Scale Introduction Logarithmic decrement, (δ) is used to find the damping ratio of an under-damped system in the time domain. The logarithmic decrement is the natural log of the ratio of the amplitudes of the first two successive peaks Logarithmic decrement is given by δ=lnX1X2 If we consider the drop in amplitude in n successive cycles then the log decrement is given by δ=1nlnX0Xn The damping ratio is a parameter, usually denoted by ζ (zeta) that characterizes the frequency response of a second order ordinary differential equation. Damping ratio (ζ) can be calculated by ζ=δ2π Oscillation frequency (fn) can be calculated by fn=1T Angular velocity ωn can be calculated by ωn=2πfn Damping coefficient (c) can be calculated by c=2ζωnm This accelerometer records data in lowest significant bit and it has a 10-bit resolution. The range for this device is ±4g. This means that the resolution is: 210=1024 bits ±4g = 8g 1024 bits/8g = 128bits/g Procedure Part 1: No Damper Attached: (If your lab equipment has the damper already attached, please do Part 2 first, and come back to Part 1 afterwards) 1. Measure the mass of the vibrating beam and record it 2. Measure the mass of the attachments on the beam and record it 3. Measure the mass of the clamps and record it Items | Mass (kg) | Mass of Aluminum Beam | 330 g | 1/3 Mass of

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