# Earthquake Engineering Questions and Answers – Dynamics of Two Degree Freedom System

This set of Earthquake Engineering Multiple Choice Questions & Answers (MCQs) focuses on “Dynamics of Two Degree Freedom System”.

1. Which of the following is not a component of every dynamic system?
a) A mechanism for storing strain energy
b) Mechanism for storing kinetic energy
c) Mechanism to measure the velocity
d) An energy dissipation mechanism

Explanation: There is no mechanism to measure the velocity in any dynamic system. The mass element (m) stores the kinetic energy and it is also responsible for generation of inertia forces. The spring element (k) stores the potential energy and it is responsible for generation of elastic restoring forces. The dashpot (c) represents the damper for dissipation or loss of energy.

2. Which of the following inferences can be drawn from the stability and accuracy considerations?
a) Positive real eigenvalues lead to a change in sign
b) Negative real eigenvalues do not lead to change in sign at each step
c) Complex eigenvalues do not lead to change in sign
d) If modulus of eigenvalue is smaller then 1, the involution converges towards zero

Explanation: The involution converges towards zero for modulus of eigenvalue is smaller then 1, is the only correct inferences drawn from the stability and accuracy considerations. Other inferences are Positive real eigenvalues do not lead to a change in sign, Negative real eigenvalues lead to change in sign at each step and Complex eigenvalues may lead to change in sign depending on each step.

3. Duhamel integral is applicable for both linear and nonlinear systems.
a) True
b) False

Explanation: Duhamel integral is an approach to evaluate the dynamic response of SDOF systems. Duhamel integral involves interpolation of the integrand and therefore, is strictly applicable for linear systems only. The second approach by approximation of the derivatives in the differential equations of motions is applicable for both linear and nonlinear systems.

4. For what value of modulus of all eigenvalues, stability is ensured?
a) Modulus of eigenvalues = 5
b) Modulus of eigenvalues > 1
c) Modulus of eigenvalues < 1
d) Modulus of eigenvalues = 2

Explanation: If we want the stability to be ensured, the modulus of eigenvalues should be less than 1. In this case, the algorithm would simulate a damped motion which is often referred to as algorithmic damping. To achieve a satisfactory performance, the presence of complex eigenvalues with a modulus of 1 is necessary.

5. Which type of nature of damping force is assumed in a 2-DOF system?
a) Coulomb
b) Viscous
c) Dry friction
d) Slip

Explanation: The nature of damping force is assumed to be of the viscous type. They are an approximate representation of the combined action of all energy dissipation mechanisms present in a vibrating system. Precise nature of damping force is not very important for dynamic response computations.

6. For critical damping in the range of 5-10%, which of the following is true?
a) Maximum spectral acceleration is of the order of 1.5 times the maximum ground acceleration
b) Maximum spectral velocity is of the same order as the maximum ground velocity
c) Maximum spectral displacement is of the same order as the maximum ground displacement
d) Maximum spectral displacement is of the order of twice the maximum ground displacement

Explanation: For critical damping in the range of 5-10%, Maximum spectral displacement is of the same order as the maximum ground displacement, maximum spectral velocity is of the order 1.5 times the maximum ground velocity and maximum spectral acceleration is of the order of 2 times the maximum ground acceleration.

7. According to the deformation characteristics, what do you call the buildings, if the floor moves only in the horizontal direction without any rotation of horizontal section?
a) Moment buildings
b) Moment-shear buildings
c) Damped buildings
d) Shear buildings

Explanation: Buildings are basically divided into two groups based on their deformation characteristics. If the floor moves only in horizontal direction and there is no rotation of a horizontal section, it is termed as shear buildings. If the floor moves in both horizontal and rotational directions, they are referred to as moment-shear buildings.

Sanfoundry Global Education & Learning Series – Earthquake Engineering.

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