Consider a damped mass on a spring driven by a sinusoidal, externally applied force. (This is called a driven, damped harmonic oscillator and is common in aeroelastic structures like wings.) The resonant frequency in rad/s of this type of oscillator is: where the spring constant , the mass , and the damping coefficient are typically aspects of your system you can design. However, due to manufacturing variability, you do not have exact control over . Instead is normally distributed with mean kg/s and standard devation kg/s. If N/m and kg: What is mean and standard deviation of the resonant frequency? You want to make sure that there is no more than an 21.71% probability that the resonant frequency is between 0.6153 and 0.7653. How tight of a tolerance do you need to ask your supplier to put on (assuming you can't change its mean) to achieve this? (Express your answer as a new standard deviation for (i. e., )). Hint: For this question you can assume the resonant frequency is normally distributed.

Describe how the presence of possible outliers might be identified on the following. (a) histograms gap between the first bar and the rest of bars or between the last bar and the rest of bars large group of bars to the left or right of a gap higher center bar than surrounding bars gap around the center of the histogram higher far left or right bar than surrounding bars (b) dotplots large gap around the center of the data large gap between data on the far left side or the far right side and the rest of the data large groups of data to the left or right of a gap large group of data in the center of the dotplot large group of data on the left or right of the dotplot (c) stem-and-leaf displays several empty stems in the center of the stem-and-leaf display large group of data in stems on one of the far sides of the stem-and-leaf display large group of data near a gap several empty stems after stem including the lowest values or before stem including the highest values large group of data in the center stems (d) box-and-whisker plots data within the fences placed at q1 â’ 1.5(iqr) and at q3 + 1.5(iqr) data beyond the fences placed at q1 â’ 2(iqr) and at q3 + 2(iqr) data within the fences placed at q1 â’ 2(iqr) and at q3 + 2(iqr) data beyond the fences placed at q1 â’ 1.5(iqr) and at q3 + 1.5(iqr) data beyond the fences placed at q1 â’ 1(iqr) and at q3 + 1(iqr)