A force of 39 N is needed to keep a spring with a 8 kg mass stretched 0.75 m beyond its natural length. For the problem above, find the damping constant c that would produce critical damping. c = ________

A force of 39 N is needed to keep a spring with a 8 kg mass stretched 0.75 m beyond its natural length. For the problem above, find the damping constant c that would produce critical damping. c = ________

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

Suppose that the vertical position axis x is oriented upward A shell of mass 2 kg is shot upward with an initial velocity of 100 m/sec. The magnitude of the force due to air resistance is with x = 0 at ground level. Denote by x(t) and v(t) the position and velocity of the shell at time t (in seconds). The acceleration due to gravity has magnitude g=9.81 m/sec². 20 The following numerical values might be useful in the calculations: In 1.96= 0.764, In 98.04 =4.58, In 392.4 = 5.97, In 492.4 = 6.20 (a) Find the differential equation satisfied by v(t) O A. dv V + dt 40 = -9.81
A belt of mass m per unit length is partly wound aroúnd a pully. The power p transmitted is given by p = Tv² – 2mv³3 where T is the tension and v the velcoity. Determine the velocity v for which maximum power transmission occurs. Evaluate this for T= 7.14 and m = 8.71. Give your answer to 2 decimal places.
At time 0, Cheryl deposits X into a bank account that credits interest at an annual effective rate of 6%. At time 3, Gomer deposits 10000 into a different bank account that credits simple interest at an annual rate of y%. At time 5, the annual forces of interest on the two accounts are equal, and Gomer's account has accumulated to Z. Calculate Z.
5. At time t = 0 a ball is thrown straight up at 208 feet per second from the top of a 2688 foot tall building. Assuming Earth's gravity is a(t) = –32 feet per second²: a. Find the position and velocity functions of the ball. Be sure to label which is which. b. What is the ball's maximum height above the ground? c. When does the ball hit the ground?
A spring with a 2-kg mass and a damping constant 2 can be held stretched 2.5 meters beyond its natural length by a force of 7.5 newtons. Suppose the spring is stretched 5 meters beyond its natural length and then released with zero velocity, In the notation of the text, what is the value c² 4mk? 2 m²kg²/sec² Find the position of the mass, in meters, after t seconds. Your answer should be a function of the variable t with the general form cos(ßt) + c₂ert sin(8t) eat C1 α= ß = Y = 8 = - C1 = C₂ =
Find undamped position too