MANE $4900-$ Aeroelasticity and Structural Vibrations

Homework $1-$ Due Jan. $20,2023$

Consider a $100g,1m$ long uniform string. If I want the string's first natural frequency of vibration to be $440Hz,$ how much tension must I apply to the string?

Given your solution to problem $1,$ what are the second and third natural frequencies of this string?

What will the steady deformation of this string under the influence of gravity? Assume that the string is oriented such that gravity acts perpendicular to the length of the string. $($Hint: Set the acceleration to zero$).$