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A 10 kilogram object suspended from the end of a vertically hanging spring stretches the spring 9.8 centimeters. At time ?=0, the resulting mass-spring system is disturbed from its rest state by the force ?(?)=100cos(10?). The force ?(?) is expressed in Newtons and is positive in the downward direction, and time is measured in second

A 10 kilogram object suspended from the end of a vertically hanging spring stretches the spring 9.8 centimeters. At time ?=0, the resulting mass-spring system is disturbed from its rest state by the force ?(?)=100cos(10?). The force ?(?) is expressed in Newtons and is positive in the downward direction, and time is measured in second

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A 10 kilogram object suspended from the end of a vertically hanging spring stretches the spring 9.8 centimeters. At time ?=0, the resulting mass-spring system is disturbed from its rest state by the force ?(?)=100cos(10?). The force ?(?) is expressed in Newtons and is positive in the downward direction, and time is measured in seconds.

a. Determine the spring constant k. By Hooke's law, the spring constant k is equal to the magnitude (absolute value) of the force exerted by the object pulling the spring down, divided by the distance (in meters) that the spring is stretched. The force exerted by the object is equal to its mass in kilograms multiplied by the magnitude (absolute value) of the acceleration of gravity, 9.8m/s. The units of force are Newtons. k = Newtons / meter b. Formulate the initial value problem for y(t), where y(t) is the displacement of the object from its equilibrium rest state, measured positive in the downward direction. (Give your answer in terms of y, y', y", t. Differential equation: help (equations) Initial conditions: y(0) = and y'(0) = help (numbers) For the initial conditions in this problem and the next one, be aware that the spring started off suspended (not moving) at its rest position. c. Solve the initial value problem for y(t). y(t) = help (formulas) d. Plot the solution and determine the maximum excursion from equilibrium made by the object on the time interval 0 <t< oo. If there is no such maximum, enter NONE. maximum excursion = meters help (numbers)
Transcribed Image Text:a. Determine the spring constant k. By Hooke's law, the spring constant k is equal to the magnitude (absolute value) of the force exerted by the object pulling the spring down, divided by the distance (in meters) that the spring is stretched. The force exerted by the object is equal to its mass in kilograms multiplied by the magnitude (absolute value) of the acceleration of gravity, 9.8m/s. The units of force are Newtons. k = Newtons / meter b. Formulate the initial value problem for y(t), where y(t) is the displacement of the object from its equilibrium rest state, measured positive in the downward direction. (Give your answer in terms of y, y', y", t. Differential equation: help (equations) Initial conditions: y(0) = and y'(0) = help (numbers) For the initial conditions in this problem and the next one, be aware that the spring started off suspended (not moving) at its rest position. c. Solve the initial value problem for y(t). y(t) = help (formulas) d. Plot the solution and determine the maximum excursion from equilibrium made by the object on the time interval 0 <t< oo. If there is no such maximum, enter NONE. maximum excursion = meters help (numbers)
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