Proof that it follows from the solution obtained that

Reference no: EM13550423

A body of mass m kg attached to a spring moves with friction. The motion is described by the second Newton's law: m(d^2y/dt^2) + a(dy/dt) + ky = 0 where y is the body displacement in m, t is the time in s, a > 0 is the friction coeffcient in kg/s and k is the spring constant in kg/s2. Assuming m = 1 kg and k = 4 kg/s2, find:

a) What is the range of values of a for which the body moves (i) with oscillations, (ii) without oscillations?

b) Find the general solution for any a < 4. (Your solution should be a formula depending on the parametera.) Proof that it follows from the solution obtained that the body slows down to a virtually rest state at large time (i.e. when t --> infinity)?

c) Find the particular solution for a = 4 subject to the initial conditions y(0) = 0, dy/dt = 1 m/s at t = 0. Plot this solution and determine the largest displacement of the mass using calculus.

Reference no: EM13550423

Questions Cloud

Water is observed to be seeped through this slope at a rate : The relative density of a sloped sand deposit is known to be 75%. Water is observed to be seeped through this slope at a rate such that the discharge velocity is 0.6 m/day.

Formulate an optimization problem to help the company find : Three parallel rural routes connect two cities A and B. Traffic on these routes mainly consists of heavy trucks for a logging company, and passenger vehicle flow can be neglected. The performance functions of these three routes are

Determine the maximum moment that can be carried : Find the nominal flexural strength from part (d.) to the service capacity from part (c.). e.) Compute the ratio of the flexural strength from part (d) to the service capacity from part (c).

Calculate the height of the model : An ogee spillway of a gravity dam is to be modeled using water. The spillway section is 40 feet high, its crest length is 60 feet and the maximum discharge is 3,000 CFS when the head on the crest of the spillway is 5 feet. Using a model scale of 1:10..

Proof that it follows from the solution obtained that : Find the particular solution for a = 4 subject to the initial conditions y(0) = 0, dy/dt = 1 m/s at t = 0. Plot this solution and determine the largest displacement of the mass using calculus.

Determine the carburizing time necessary to achieve a carbon : Determine the carburizing time necessary to achieve a carbon concentration of 0.35 wt% at a position 2 mm into an iron–carbon alloy that initially contains 0.10 wt% C

How long will it take for the concentration to be one-quarte : A batch system is assumed to be first order. The initial concentration is 225 mg/L. If the reaction rate constant is 0.65 hr^-1, how long will it take for the concentration to be one-quarter the starting concentration?

Determine the reaction rate constant : A reaction in a batch system is assumed to be first order. Data listed below was collected. Determine the reaction rate constant.

Calculate the mass flux rate and the flow rate : During a drilling operation, the small robotic device is subjected to an (F =) 900 N force at point C as shown. (? = 25°.) Replace this force by an equivalent force-couple system at point O.

User Account

All Pages