Question

Consider the vertical oscillation of the system of springs and masses shown below with the spring constants $K_A = 78 ext{ Nm}^{-1}$, $K_B = 15 ext{ Nm}^{-1}$ and $K_C = 6 ext{ Nm}^{-1}$. The system shown here is after the influence of gravitational force. So, all the masses are at their equilibrium position. Take mass $m_1 = 1 ext{ kg}$ and $m_2$ to be $3 ext{ kg}$. (a) Find the equations of motions and hence write the equations of motions in matrix form. 4 points (b) Calculate the normal frequencies, normal modes and hence the positions of the blocks as a function of time up to few undetermined constants. 3+3+1 points (c) Calculate the normal coordinates. 4 points (d) If the $m_1$ block is displaced up 1m from its equilibrium position with the $m_2$ block held at its equilibrium position and both blocks released from rest, describe the subsequent motion of both blocks. 5 points

          Consider the vertical oscillation of the system of springs and masses shown below with the spring constants $K_A = 78 	ext{ Nm}^{-1}$, $K_B = 15 	ext{ Nm}^{-1}$ and $K_C = 6 	ext{ Nm}^{-1}$. The system shown here is after the influence of gravitational force. So, all the masses are at their equilibrium position. Take mass $m_1 = 1 	ext{ kg}$ and $m_2$ to be $3 	ext{ kg}$.

(a) Find the equations of motions and hence write the equations of motions in matrix form.
4 points
(b) Calculate the normal frequencies, normal modes and hence the positions of the blocks as a function of time up to few undetermined constants.
3+3+1 points
(c) Calculate the normal coordinates.
4 points
(d) If the $m_1$ block is displaced up 1m from its equilibrium position with the $m_2$ block held at its equilibrium position and both blocks released from rest, describe the subsequent motion of both blocks.
5 points

Consider the vertical oscillation of the system of springs and masses shown below with the spring constants KA = 78 ext Nm^-1, KB = 15 ext Nm^-1 and KC = 6 ext Nm^-1. The system shown here is after the influence of gravitational force. So, all the masses are at their equilibrium position. Take mass m1 = 1 ext kg and m2 to be 3 ext kg.

(a) Find the equations of motions and hence write the equations of motions in matrix form.
4 points
(b) Calculate the normal frequencies, normal modes and hence the positions of the blocks as a function of time up to few undetermined constants.
3+3+1 points
(c) Calculate the normal coordinates.
4 points
(d) If the m1 block is displaced up 1m from its equilibrium position with the m2 block held at its equilibrium position and both blocks released from rest, describe the subsequent motion of both blocks.
5 points

Added by Carmen T.

Question

Please give Ace some feedback