Which of the following statement(s) is/are true about harmonically excited forcedvibration of a single degree-of-freedom linear spring-mass-damper system?(A) The total response of the mass is a combination of free vibration transient andsteady-state response.(B) The free vibration transient dies out with time for each of the three possibleconditions of damping (under-damped, critically damped, and over-damped).(C) The steady-state periodic response is dependent on the initial conditions at thetime of application of external forcing.(D) The rate of decay of free vibration transient response depends on the mass, springstiffness and damping constant.Q.26 Which of the following statement(s) is/are true about the state of stress in a plane?(A) Maximum or major principal stress is algebraically the largest direct stress at apoint.(B) The magnitude of minor principal stress cannot be greater than the magnitude ofmajor principal stress.(C) The planes of maximum shear stress are inclined at 90 degrees to the principalaxes.(D) The normal stresses along the planes of maximum shear stress are equal.
Question
Which of the following statement(s) is/are true about harmonically excited forcedvibration of a single degree-of-freedom linear spring-mass-damper system?(A) The total response of the mass is a combination of free vibration transient andsteady-state response.(B) The free vibration transient dies out with time for each of the three possibleconditions of damping (under-damped, critically damped, and over-damped).(C) The steady-state periodic response is dependent on the initial conditions at thetime of application of external forcing.(D) The rate of decay of free vibration transient response depends on the mass, springstiffness and damping constant.Q.26 Which of the following statement(s) is/are true about the state of stress in a plane?(A) Maximum or major principal stress is algebraically the largest direct stress at apoint.(B) The magnitude of minor principal stress cannot be greater than the magnitude ofmajor principal stress.(C) The planes of maximum shear stress are inclined at 90 degrees to the principalaxes.(D) The normal stresses along the planes of maximum shear stress are equal.
Solution
(A) The total response of the mass is a combination of free vibration transient and steady-state response. (B) The free vibration transient dies out with time for each of the three possible conditions of damping (under-damped, critically damped, and over-damped). (C) The steady-state periodic response is dependent on the initial conditions at the time of application of external forcing. (D) The rate of decay of free vibration transient response depends on the mass, spring stiffness, and damping constant.
To determine which statement(s) is/are true about the harmonically excited forced vibration of a single degree-of-freedom linear spring-mass-damper system, we can analyze each statement individually:
(A) The total response of the mass is a combination of free vibration transient and steady-state response. This statement is true. The total response of the mass in a harmonically excited forced vibration includes both the initial free vibration transient and the steady-state response.
(B) The free vibration transient dies out with time for each of the three possible conditions of damping (under-damped, critically damped, and over-damped). This statement is true. The free vibration transient, which represents the initial response of the system after the external forcing is applied, will eventually die out with time for all three conditions of damping.
(C) The steady-state periodic response is dependent on the initial conditions at the time of application of external forcing. This statement is false. The steady-state periodic response of a harmonically excited forced vibration is not dependent on the initial conditions. It is solely determined by the frequency and amplitude of the external forcing.
(D) The rate of decay of free vibration transient response depends on the mass, spring stiffness, and damping constant. This statement is true. The rate of decay of the free vibration transient response is influenced by the properties of the system, including the mass, spring stiffness, and damping constant.
In summary, the true statements about harmonically excited forced vibration of a single degree-of-freedom linear spring-mass-damper system are:
- (A) The total response of the mass is a combination of free vibration transient and steady-state response.
- (B) The free vibration transient dies out with time for each of the three possible conditions of damping (under-damped, critically damped, and over-damped).
- (D) The rate of decay of free vibration transient response depends on the mass, spring stiffness, and damping constant.
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