Consider the spring-mass-damper system response show in the graph below: Select
ID: 3111134 • Letter: C
Question
Consider the spring-mass-damper system response show in the graph below: Select the 3 statements that are true about the spring-mass-damper system and its response graph. A. The spring-mass-damper system is underdamped. B. The spring-mass-damper system has both a steady-state solution and a transient solution. C. The spring-mass-damper system has an initial position of x = 0. D. The spring-mass-damper system has a driving force with amplitude 1 and frequency near 1. E. The spring-mass-damper system is overdamped.Explanation / Answer
From the given solution curve, we can tell one thing for sure that the solution is combination of a decreasing exponential function and a sinusoidal function.
The solution of a second order differential equation is combination of a decreasing exponential function and a sinusoidal function only when the roots of the characteristic equation are complex with negative real part.
Considering these facts, let us now look at the given options:
A) This option is true as we know that roots of characteristic equation are complex, which implies that determinant is negative and therefore, system is underdamped
B) Since homogeneous solution is not zero (it is 1). Therefore, solution has both transient and homogeneous parts. Hence this statement is true as wel.
C) Since the solution starts at (t,x) = (0,0), therefore, this statement is true as well.
D) False
E) False