Question

B3. A system of two masses linked through a damper and a spring shown in Figure B3 is acted upon by a control input (force) $u$. $m = 1$ kg, $M = 2$ kg, $c = 10$ Ns/m and $k = 10$ kN/m. (a) Derive the equations of motion for this open-loop system and its transfer matrix. (b) Convert the above equations into the state-space formulation in matrix form. (c) Find out whether this system is stable and why.

          B3.
A system of two masses linked through a damper and a spring shown in Figure B3 is acted
upon by a control input (force) $u$. $m = 1$ kg, $M = 2$ kg, $c = 10$ Ns/m and $k = 10$ kN/m.
(a) Derive the equations of motion for this open-loop system and its transfer matrix.
(b) Convert the above equations into the state-space formulation in matrix form.
(c) Find out whether this system is stable and why.

B3.
A system of two masses linked through a damper and a spring shown in Figure B3 is acted
upon by a control input (force) u. m = 1 kg, M = 2 kg, c = 10 Ns/m and k = 10 kN/m.
(a) Derive the equations of motion for this open-loop system and its transfer matrix.
(b) Convert the above equations into the state-space formulation in matrix form.
(c) Find out whether this system is stable and why.

Added by Andre N.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Lainey Roebuck

Step 1

For the mass m: Fcu - Fd - Fs = m * am where Fcu is the control input force, Fd is the damping force, Fs is the spring force, and am is the acceleration of mass m. For the mass M: -Fd - Fs = M * aM where aM is the acceleration of mass M. Now, let's express the Show more…

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B3. A system of two masses linked through a damper and a spring shown in Figure B3 is acted upon by a control input forccu.m = 1 kg, M = 2 kg, c = 10 Ns/m, and k = 10 kN/m. Figure B3 a) Derive the equations of motion for this open-loop system and its transfer matrix. [12] (b) Convert the above equations into the state-space formulation in matrix form. [9] (c) Find out whether this system is stable and why. [4]