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An object of mass 3 grams hanging at the bottom of a spring with a spring constant 4 grams per second square. Denote by y vertical coordinate, positive downwards, and y = 0 is the spring-mass resting position. (a) Write the differential equation y" = f(y, y') satisfied by this system. f(y, y) = Σ Σ v(1) T Note: Write t for t, write y for y(t), and yp for y' (t). (b) Find the mechanical energy E of this system. E(t) = Note: Write t for t, write y for y(t), and yp for y' (t). (c) If the initial position of the object is y(0) = -2 and its initial velocity is y'(0) = 3, find the maximum value of the position of the object, max>0, achieved during its motion. Упх= Σ

An object of mass 3 grams hanging at the bottom of a spring with a spring constant 4 grams per second square. Denote by y vertical coordinate, positive downwards, and y = 0 is the spring-mass resting position. (a) Write the differential equation y" = f(y, y') satisfied by this system. f(y, y) = Σ Σ v(1) T Note: Write t for t, write y for y(t), and yp for y' (t). (b) Find the mechanical energy E of this system. E(t) = Note: Write t for t, write y for y(t), and yp for y' (t). (c) If the initial position of the object is y(0) = -2 and its initial velocity is y'(0) = 3, find the maximum value of the position of the object, max>0, achieved during its motion. Упх= Σ

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An object of mass 3 grams hanging at the bottom of a spring with a spring constant 4 grams per second square. Denote by y vertical coordinate, positive downwards, and y = 0 is the spring-mass resting position. (a) Write the differential equation y" = f(y, y') Note: Write t for t, write y for y(t), and yp for y' (t). (b) Find the mechanical energy E of this system. E(t) = Note: Write t for t, write y for y(t), and yp for y' (t). (c) If the initial position of the object is y(0) = -2 and its initial velocity is y' (0) = 3, find the maximum value of the position of the object, ymax > 0, achieved during its motion. Σ Umax = f(y, y') satisfied by this system. Σ Į m y(t) Σ
Transcribed Image Text:An object of mass 3 grams hanging at the bottom of a spring with a spring constant 4 grams per second square. Denote by y vertical coordinate, positive downwards, and y = 0 is the spring-mass resting position. (a) Write the differential equation y" = f(y, y') Note: Write t for t, write y for y(t), and yp for y' (t). (b) Find the mechanical energy E of this system. E(t) = Note: Write t for t, write y for y(t), and yp for y' (t). (c) If the initial position of the object is y(0) = -2 and its initial velocity is y' (0) = 3, find the maximum value of the position of the object, ymax > 0, achieved during its motion. Σ Umax = f(y, y') satisfied by this system. Σ Į m y(t) Σ
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