Differential equation solution: (1-3e4)sin(2 t)+(e4t - 1) cos(2 t) -4t x(t) 16
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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 posi...
: When a 3 kg mass is attached to a spring whose constant is 12 N/m,...
: 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,...
: 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 5 kg mass is attached to a spring whose constant is 45 N/m, it...
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 4 kg mass is attached to a spring whose constant is 100 N/m, it...
When a 4 kg mass is attached to a spring whose constant is 100 N/m, it comes to rest in the equilibrium position. Starting at t= 0, a force equal to f(t) = 12e-3t 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...
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...
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...
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?
1) When a mass of 3 kilograms is attached to a spring whose constant is 48...
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) =
6. A mass of 2 kilogram is attached to a spring whose constant is 4 N/m, and the entire system is...
6. A mass of 2 kilogram is attached to a spring whose constant is 4 N/m, and the entire system is then submerged in a liquid that inparts a damping force equal to 4 tines the instantansous velocity. At t = 0 the mass is released from the equilibrium position with no initial velocity. An external force t)4t-3) is applied. (a) Write (t), the external force, as a piecewise function and sketch its graph b) Write the initial-value problem (c)Solve...
A spring-mass system has a spring constant of 3 N/m. A mass of 2 kg is...
A spring-mass system has a
spring constant of 3 N/m. A mass of 2 kg is attached to the spring,
and the motion takes place in a viscous fluid that offers a
resistance numerically equal to the magnitude of the instantaneous
velocity. If the system is driven by an external force of (27 cos
3t − 18 sin 3t) N, determine the steady state response. Express
your answer in the form R cos(ωt − δ). (Let u(t) be the
displacement...
: 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?
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 4 kg mass is attached to a spring whose constant is 100 N/m, it comes to rest in the equilibrium position. Starting at t= 0, a force equal to f(t) = 12e-3t 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 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?
6. A mass of 2 kilogram is attached to a spring whose constant is 4 N/m, and the entire system is then submerged in a liquid that inparts a damping force equal to 4 tines the instantansous velocity. At t = 0 the mass is released from the equilibrium position with no initial velocity. An external force t)4t-3) is applied. (a) Write (t), the external force, as a piecewise function and sketch its graph b) Write the initial-value problem (c)Solve...
A spring-mass system has a
spring constant of 3 N/m. A mass of 2 kg is attached to the spring,
and the motion takes place in a viscous fluid that offers a
resistance numerically equal to the magnitude of the instantaneous
velocity. If the system is driven by an external force of (27 cos
3t − 18 sin 3t) N, determine the steady state response. Express
your answer in the form R cos(ωt − δ). (Let u(t) be the
displacement...
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