Since there is no damping the differential equation governing the mass spring system is
with
a) The aboce differential equation can be written as
--------------------(1)
The characteristic equation for this equation is
So the complementary function is
The particular solution is given by
Then,
Use in equation (1) we get
Equate coefficients we get
So we get
So the solution is
gives also
gives
At
b) The amplitude after very long time
When a 4 kg mass is attached to a spring whose constant is 100 N/m, it...
When a 6 kg mass is attached to a spring whose constant is 54 N/m, it comes to rest in the equilibrium position. Starting at 1 = 0, a force equal to f(t) = 30e-7t cos 6t is applied to the system. In the absence of damping. (a) find the position of the mass when t=1. (b) what is the amplitude of vibrations after a very long time?
When a 6 kg mass is attached to a spring whose constant is 54 N/m, it comes to rest in the equilibrium position. Starting at i = 0, a force equal to f(0) = 30e-7t cos 6t is applied to the system. In the absence of damping, (a) find the position of the mass when t= 1. (b) what is the amplitude of vibrations after a very long time?
When a 6 kg mass is attached to a spring whose constant is 54 N/m, it comes to rest in the equilibrium position. Starting at i = 0, a force equal to f(0) = 30e-7t cos 6t is applied to the system. In the absence of damping, (a) find the position of the mass when t= 1. (b) what is the amplitude of vibrations after a very long time?
When a 5 kg mass is attached to a spring whose constant is 45 N/m, it comes to rest in the equilibrium position. Starting at t= 0, a force equal to f(t) 30e-3t cos 4t is applied to the system. In the absence of damping, (a) find the position of the mass when t= 1. (b) what is the amplitude of vibrations after a very long time?
: When a 3 kg mass is attached to a spring whose constant is 12 N/m, it comes to rest in the equilibrium position. Starting at i=0, a force equal to f(t) = 15e-54 cos 4t is applied to the system. In the absence of damping, (a) find the position of the mass when t=n. (b) what is the amplitude of vibrations after a very long time?
: When a 3 kg mass is attached to a spring whose constant is 12 N/m, it comes to rest in the equilibrium position. Starting at i=0, a force equal to f(t) = 15e-54 cos 4t is applied to the system. In the absence of damping, (a) find the position of the mass when t=n. (b) what is the amplitude of vibrations after a very long time?
here is the question, please help me with this question When a 5 kg mass is attached to a spring whose constant is 180 N/m, it comes to rest in the equilibrium position. Starting at t= 0, a force equal to f(t) = 20e cos 3t is applied to the system. In the absence of damping, -5t (a) find the position of the mass when t=1. (b) what is the amplitude of vibrations after a very long time?
1) When a mass of 3 kilograms is attached to a spring whose constant is 48 N/m, it comes to rest in the equilibrium position. Starting at t = 0, a force equal to f(t) = 180e−4t cos(4t) is applied to the system. Find the equation of motion in the absence of damping. x(t) = 2) Solve the given initial-value problem. d2x dt2 + 9x = 5 sin(3t), x(0) = 6, x'(0) = 0 x(t) =
Problem #7; when a 3 kg mass is attached to a spring whose constant is 12 N/m, it comes to rest in the equilibrium position. cos 2t is applied to the system. In the absence of damping, Starting at t0, a force equal to f(t) = 18e (a) find the position of the mass when t= N. (b) what is the amplitude of vibrations after a very long time? Problem #7(a): -0.1875 Round your answer to 4 decimals. Problem #7(b):...
A 0.500 kg mass is attached to a spring of constant 150 N/m. A driving force F(t) = ( 12.0N) cos(ϝt) is applied to the mass, and the damping coefficient b is 6.00 Ns/m. What is the amplitude (in cm) of the steady-state motion if ϝ is equal to half of the natural frequency ϝ0 of the system?