What is the maximum speed vmax of the block during this motion? Find the acceleration a of the block as a function of time. Find Kmax, the maximum kinetic energy of the block.

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Author:Raymond A. Serway, Chris Vuille
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Chapter1: Units, Trigonometry. And Vectors
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  • What is the maximum speed vmax of the block during this motion?
  • Find the acceleration a of the block as a function of time.
  • Find Kmax, the maximum kinetic energy of the block.

 

To derive the formulas for the major characteristics of motion as functions of time for a
horizontal spring oscillator and to practice using the obtained formulas by answering some
basic questions.
A block of mass m is attached to a spring whose spring constant is k. The other end of the
spring is fixed so that when the spring is unstretched, the mass is located at x = 0.
(Figure 1). Assume that the +x direction is to the right.
The mass is now pulled to the right a distance A beyond the equilibrium position and
released, at time t = 0, with zero initial velocity.
Assume that the vertical forces acting on the block balance each other and that the tension
of the spring is, in effect, the only force affecting the motion of the block. Therefore, the
system will undergo simple harmonic motion. For such a system, the equation of motion is
a(t) = − x(t).
and its solution, which provides the equation for ™ (t), is
r(t) = A cos (√√t).
Transcribed Image Text:To derive the formulas for the major characteristics of motion as functions of time for a horizontal spring oscillator and to practice using the obtained formulas by answering some basic questions. A block of mass m is attached to a spring whose spring constant is k. The other end of the spring is fixed so that when the spring is unstretched, the mass is located at x = 0. (Figure 1). Assume that the +x direction is to the right. The mass is now pulled to the right a distance A beyond the equilibrium position and released, at time t = 0, with zero initial velocity. Assume that the vertical forces acting on the block balance each other and that the tension of the spring is, in effect, the only force affecting the motion of the block. Therefore, the system will undergo simple harmonic motion. For such a system, the equation of motion is a(t) = − x(t). and its solution, which provides the equation for ™ (t), is r(t) = A cos (√√t).
0=x
-X
A
Transcribed Image Text:0=x -X A
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