What is the range of values of a for which the body moves

Reference no: EM13316881

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 parameter a.) 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: EM13316881

Questions Cloud

What is the velocity of the cannon ball : A cannon with mass of 2000kg fires a 10kg shell at an angle of 60 degrees above the horizontal. what is the velocity of the cannon ball

Design and implementation of a security approach : use Microsoft Powerpoint to create your slides for a 15-minute presentation. It`s about Computer Hacking the same subject that you wrote in the report. You are going to take the same information that you wrote in the report and make it as slides.

What minimum applied force is needed to open the gate : A rectangular gate is inclined at an angle of 30 degrees from the horizontal. It is 4 ft wide by 6 feet long. If it is hung from its upper end which is 8 feet below the waters top edge, what minimum applied force (bottom) is needed to open the gat..

How much louder does the traffic noise seem : When the decibel of traffic in the street goes from 40 to 60 dB, How much louder does the traffic noise seem

What is the range of values of a for which the body moves : 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.

Calculate the water pressure on the second floor : The water pressure in the pipes in the basement of a tall house is 5.1 105 Pa. Calculate the water pressure on the second floor

Determine the reaction rate constant to be first order : A reaction in a batch system is assumed to be first order. Data listed below was collected. Determine the reaction rate constant. chemical concentration (ug/L) time(min) 19.3 6

Find the change in mechanical energy of the elevator : 2000 kg elevator is accelerated uniformly from rest to 4 m/s in a time of 90s. find the change in mechanical energy of the elevator

What category information is collected by the site : Information has many facets: value, confidentiality, integrity, privacy, legality, and so on. All information is not the same and hence its protection requirements may vary.

User Account

All Pages