SDOF - Lesson 1

Question 1

what does SDOF stand for?

Answer 1

Simple Degree of Freedom

Question 2

Unit of M: MASS

Answer 2

Kg

Question 3

Unit of K: STIFFNESS

Answer 3

N/m

Question 4

Unit of c: viscous DAMPING coefficient

Answer 4

Ns/m

Question 5

F_d_arrow =

Answer 5

-cdeltax_dot_arrow

Question 6

F_e_arrow=

Answer 6

-Kdeltax_dot_arrow

Question 7

vibrations: position x measured from equilibrium (displacement)

Question 8

If REFERENCE FRAME x(t), x_dot, x_dot_dot go right. What happen to FBD on a body with clamped spring and clamped damping on left and right side?

Answer 8

LEFT:
K_1x AND K_2x
c_1x_dot AND c_2x_dot
m*x_dot_dot

DOWN:
mg

UP:
Normal force

Question 9

INERTIA FORCE F_i_arrow=

Answer 9

-m*x_dot_dot

Question 10

Solution of a dynamic problem as a force balance
(Where SUM(F_j_arrow) is NET FORCE)

Answer 10

SUM(F_j_arrow) + F_i_arrow = 0

Question 11

ODE (Ordinary Differential EQ.) 2nd ORDER

Answer 11

mx_dot_dot +(c_1+c_2)x_dot+(K_1+K_2)*x=0

Question 12

EQ. of motion of SDOF TRANSCATIONAL system

Answer 12

mx_dot_dot +cx_dot+K*x=0

Question 13

TORSIONAL or angular oscillations
Unit of K_t: TORSIONAL STIFFNESS

Answer 13

Nm/rad

Question 14

TORSIONAL or angular oscillations
Unit of c_t: TORSIONAL VISCOUS DAMPING COEFFICIENT

Answer 14

Nms/rad

Question 15

Unit of I_G: MASS MOMENT OF INERTIA
(About an axis passing through G, where G is the centre of mass

Answer 15

kg*m^2

Question 16

Theta =

Answer 16

Generalized coordinate. Angular displacement from equilibrium configuration

Question 17

FBD of ROTATING MASS - DISK OF FLYWHEEL. If REFERENCE FRAME theta, theta_dot, theta_dot_dot go CLOCKWISE. What happen to FBD on a body

Answer 17

COUNTER CLOCKWISE:
K_ttheta
c_ttheta_dot
I_G*theta_dot_dot

Question 18

CANONICAL/STANDARD FORM of SDOF vibrating system

Answer 18

x_dot_dot+2XIOmega_nx_dot + Omega^2_nx=0

x_dot_dot+(c/m)x_dot+(K/m)x=0

Question 19

Unit of Omega_n: ANGULAR NATURAL FREQUENCY

Answer 19

RAD/s

Question 20

Unit of XI: Damping FACTOR or damping Ratio

Answer 20

no unit

Question 21

Omega_n=

Answer 21

sqrt(K/m)

Question 22

XI=

Answer 22

c/(2mOmega_n)

Question 23

Unit of f_n: natural frequency

Answer 23

Hz = cycle/s

Question 24

f_n=

Answer 24

Omega_n/(2*pi)

Question 25

EXAMPLE:
Initial conditions: x_0=x(t=0)=0
x_0_dot=V(t=0)=V_0

Undamped: XI=0

SYSTEM RESPONSE: CONSTANT AMPLITUDE SINE WAVE

x and XI vertical axis
t horizontal axis

x_0: origo
V_0: tangent angle through x_0 and sin curve