Sliding movement with a motor. A heavy block of mass 1 kg is placed on a flat surface and attached to a horizontal spring. When the block is displaced 25 cm to the right of its equi- librium position the spring exerts a restoring force of 1 Newton to the left. Friction acts on the block proportional to its velocity such that when its speed is 1 m/s the block expe- riences a drag force of 4 Newtons. At time t = 0 seconds the block is at its equilibrium position traveling with a velocity of 1 m/s (i.e., traveling to the right). At t = 1 seconds a motor is switched on which exerts a force of t - 1 Newtons on the block. At t = 4 seconds the motor is switched off, and no external force acts on the block thereafter. (a) Rewrite the forcing function g(t) for the problem using unit step functions uc (t). Your answer should be expressible as a linear combination of uc(t)'s for different c's, each multiplied by some function of t. (b) Write down the initial value problem that models the horizontal position x(t) of the block, measured from its equilibrium position, for t≥ 0. (c) Find the Laplace transform X(s) of the solution of the initial-value problem from part (b). No need to find x(t).

Sliding movement with a motor. A heavy block of mass 1 kg is placed on a flat surface and attached to a horizontal spring. When the block is displaced 25 cm to the right of its equi- librium position the spring exerts a restoring force of 1 Newton to the left. Friction acts on the block proportional to its velocity such that when its speed is 1 m/s the block expe- riences a drag force of 4 Newtons. At time t = 0 seconds the block is at its equilibrium position traveling with a velocity of 1 m/s (i.e., traveling to the right). At t = 1 seconds a motor is switched on which exerts a force of t - 1 Newtons on the block. At t = 4 seconds the motor is switched off, and no external force acts on the block thereafter. (a) Rewrite the forcing function g(t) for the problem using unit step functions uc (t). Your answer should be expressible as a linear combination of uc(t)'s for different c's, each multiplied by some function of t. (b) Write down the initial value problem that models the horizontal position x(t) of the block, measured from its equilibrium position, for t≥ 0. (c) Find the Laplace transform X(s) of the solution of the initial-value problem from part (b). No need to find x(t).

Mathematics For Machine Technology

8th Edition

ISBN:9781337798310

Author:Peterson, John.

Publisher:Peterson, John.

Chapter61: Areas Of Circles, Sectors, And Segments

Section: Chapter Questions

Problem 20A: Hydraulic pressure of 705.0 pounds per square inch is exerted on a 3.150-inch diameter piston. Find...

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