a. 4b. Draw a free body diagram and write a governing equation for y in the...

  

Transcribed Image Text:

a. 4b. Draw a free body diagram and write a governing equation for y in the system below. Let y = 0 when the spring is relaxed, and assume that gravity acts in the -y direction. By f(t) m k B Suppose the location of the mass were measured using a new variable z: mg k z(t) = y(t) + 4c. where g is gravitational acceleration (note that mg/k is a constant). Use the above definition to write expressions for y, y, and in terms of z and its derivatives. y = y = = Now rewrite your governing equation from part (a) in terms of z and its derivatives, and reorganize. Do you think the equation looks mathematically easier to solve using y or z? **Any constant force exerted on a spring can be treated in this way. a. 4b. Draw a free body diagram and write a governing equation for y in the system below. Let y = 0 when the spring is relaxed, and assume that gravity acts in the -y direction. By f(t) m k B Suppose the location of the mass were measured using a new variable z: mg k z(t) = y(t) + 4c. where g is gravitational acceleration (note that mg/k is a constant). Use the above definition to write expressions for y, y, and in terms of z and its derivatives. y = y = = Now rewrite your governing equation from part (a) in terms of z and its derivatives, and reorganize. Do you think the equation looks mathematically easier to solve using y or z? **Any constant force exerted on a spring can be treated in this way.