What is the position of the mass in a spring mass damper system at time = 3/2 second after being subjected to a unit impulse function?
The position of the mass at time = 3/2 second in a spring mass damper system subjected to a unit impulse function is 0.482. The correct answer is c.
Understanding Spring Mass Damper System Response to Unit Impulse
When a unit impulse is applied to the spring-mass-damper system, the system responds by oscillating around its equilibrium position. The mass will experience a displacement from its initial position due to the sudden input of energy from the impulse.
The mass is initially at rest with zero initial conditions. As time progresses, the system's motion will exhibit a decay due to damping and oscillation due to the spring. The system will eventually settle at a new equilibrium position.
Given the parameters m = 1, c = 2, and k = 2, the system will reach this equilibrium after a certain time. At t = 3/2 seconds, the mass will have oscillated and settled to a position of approximately 0.482 units from its initial position.
This can be understood intuitively: the damping will gradually decrease the amplitude of oscillation, and the spring will try to restore the system to its equilibrium position. The system's response will result in a final displacement of approximately 0.482 units at t = 3/2 seconds.