A simple mass-spring oscillatory system consists of a mass m, suspended from a spring of stiffness k. Considering z as the displacement of the system at any time t, the equation of motion for the free vibration of the system is The natural frequency of the system is
The solution of the differential equation, for t > 0, y″(t) + 2y′(t) + y(t) = 0 with initial conditions y′(0) = 1and y(0) = 0, is u(t) denotes the unit step functions).
1 Crore+ students have signed up on EduRev. Have you? Download the App |
The solution to the differential equationwhere k is a constant, subjected to the boundary conditions u(0) = 0 and u(L) = U, is
A function y(t) such that y(0) = 1 and y(1) = 3e-1, is a solution of the differential equation . Then y(2) is
Consider the following statements about the linear dependence of the real valued functions y1 = 1, y2 = x and y3 = x2, over the field of real numbers.
I. y1, y2 and y3 are linearly independent on – 1 ≤ x ≤ 0
II. y1, y2 and y3 are linearly dependent on 0 ≤ x ≤ 1
III. y1, y2 and y3 are linearly independent on 0 ≤ x ≤ 1
IV. y1, y2 and y3 are linearly dependent on – 1 ≤ x ≤ 0
Which one among the following is correct?
For the Ordinary Differential Equationwith initial conditions x(0) = 0 and dx/dt(0) = 10, the solution is
If roots of the auxiliary equation ofare real and equal, the general solution of the differential equation is
The general solution of the differential equation in terms of arbitrary constants K1 and K2 is:
The complete solution of the linear differential equation
The differential equationFor y(x) with the two boundary conditions
65 videos|120 docs|94 tests
|
65 videos|120 docs|94 tests
|