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Mathematical Physics

Finding the frequency of vibration of a stretched wire.

A wire of density 9gm/cm^3 is stretched between two clamps 100cm apart subjected to an extension of 0.05 cm. What is the lowest frequency of transverse vibrations in the wire, assuming the Young's modulus to be 9x10^11 dynes/cm^ ?

Problems about Centroids III

Asking problem: Divide the parabolic spandrel shown into five vertical sections and determinate by approximate means the x coordinate of its centroids; approximate the spandrel by rectangles of the form bdd'b'. Note: The drawing file is in word97 format for PC and not for MAC. My question is how can I determine the area of

fundamental definition for centroid

The asking problem: Show that when the distance h is selected to maximize the distance Y from line BB' to the centroid of the shaded area, we also have Y=h. Note: The Y is relating to the centroid Y of the area. The drawing is in word97 format for PC and not for MAC. My problem is I don't know how can I demonstrate this. Ca

Integration practice using set limits

Three problems for practice. View the pdf file below for additional clarity. a) x^5 upper limit 1, lower limit 0 b) 3x^2 upper limit 2, lower limit 1 c) x^n upper limit 1, lower limit 0