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 v
iscous fluid that offers a resistance numerically equal to the magnitude of the instantaneous velocity. If the system is driven by an external force of (21 cos 3t − 14 sin 3t) N, determine the steady state response. Express your answer in the form R cos(ωt − δ). (Let u(t) be the displacement of the mass from its equilibrium position at time t.)
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Note: I'm not sure what do you mean by "weight 0.05 kg/L". I assume it means the mass per unit of length, so it should be "0.05 kg/m".
Solution:
The fundamental frequency in a standing wave is given by
where L is the length of the string, T the tension and m its mass. If we plug the data of the problem into the equation, we find
The wavelength of the standing wave is instead twice the length of the string:
So the speed of the wave is
And the time the pulse takes to reach the shop is the distance covered divided by the speed:
Solution:
The fundamental frequency in a standing wave is given by
where L is the length of the string, T the tension and m its mass. If we plug the data of the problem into the equation, we find
The wavelength of the standing wave is instead twice the length of the string:
So the speed of the wave is
And the time the pulse takes to reach the shop is the distance covered divided by the speed: