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Please draw the picture of the problem and explain why the author picked this initial condition in the solution

Please draw the picture of the problem and explain why the author picked this initial condition in the solution

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Please draw the picture of the problem and explain why the author picked this initial condition in the solution.

The body is hanging in its equilibrium position when it receives a sudden blow which projects it upwards with speed u. Find the subsequent motion. Solution When the spring is subjected to a constant force of magnitude mg, the extension is b. Hence a, the strength of the spring, is given by a = mg/b. Let z be the downwards displacement of the body from its equilibrium position. Then the extension of the spring is b + z and the restoring force is a(b + z) g(b+z)/b. The equation of motion for the body is therefore that is m d²z dt² where Ω (g/b)¹/2 = mg d²z + dt² b = This is the SHM equation with ² g/b. It follows that the period of vertical oscillations about the equilibrium position is given by T = b 27 (2) " In the initial value problem, the subsequent motion must have the form 2л 52 mg (b+z) b z = 0. 2π = X = - x = A cost + B sin St, where = (g/b)¹/2. The initial condition x = 0 when t = 0 shows that A = 0 and 0 then gives B = −u, that is, B -u/S2. = the initial condition x =-u whe t = The subsequent motion is therefore И 1/2 = · sin Ωt,
Transcribed Image Text:The body is hanging in its equilibrium position when it receives a sudden blow which projects it upwards with speed u. Find the subsequent motion. Solution When the spring is subjected to a constant force of magnitude mg, the extension is b. Hence a, the strength of the spring, is given by a = mg/b. Let z be the downwards displacement of the body from its equilibrium position. Then the extension of the spring is b + z and the restoring force is a(b + z) g(b+z)/b. The equation of motion for the body is therefore that is m d²z dt² where Ω (g/b)¹/2 = mg d²z + dt² b = This is the SHM equation with ² g/b. It follows that the period of vertical oscillations about the equilibrium position is given by T = b 27 (2) " In the initial value problem, the subsequent motion must have the form 2л 52 mg (b+z) b z = 0. 2π = X = - x = A cost + B sin St, where = (g/b)¹/2. The initial condition x = 0 when t = 0 shows that A = 0 and 0 then gives B = −u, that is, B -u/S2. = the initial condition x =-u whe t = The subsequent motion is therefore И 1/2 = · sin Ωt,
Example 5.1 An initial value problem for classical SHM A body of mass m is suspended from a fixed point by a light spring and can move under uniform gravity. In equilibrium, the spring is found to be extended by a distance b. Find the period of vertical oscillations of the body about this equilibrium position. [Assume small strains.]
Transcribed Image Text:Example 5.1 An initial value problem for classical SHM A body of mass m is suspended from a fixed point by a light spring and can move under uniform gravity. In equilibrium, the spring is found to be extended by a distance b. Find the period of vertical oscillations of the body about this equilibrium position. [Assume small strains.]
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