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.