# I need help in system dynamics

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Question description

i need help with my assignment and please including steps in the answer. I attached the file of the questions that need help with

1. Derive a mathematical model of the system of Figure 6 using x and  as the system outputs. 2. Consider a parallel plate capacitor. Each plate is rectangular and of dimensions 3 mm by 5 mm. A vacuum exists between the plates of the capacitor. (a) If the charge on a plate is 5.2x10-5 C and the voltage measured across the capacitor plates is 3 V. (i) What is the capacitance of the capacitor? (ii) What is the distance between the plates? (iii) What is the energy stored in the capacitor? (b) If the capacitor used in part a is used in a circuit where the current varies as i (t ) = 2.1cos 200t mA and the capacitor is uncharged at t = 0 ,(i) what is the potential difference across the capacitor as a function of time? (ii) What is the energy stored in the capacitor as a function of time? 3. For the circuit of Figure 8, vD = 30V and vF = 26 V . What are (a) the currents through each wire in the circuit, (b) The potential provided by the source, and (c) the power delivered to the circuit? 4. (a) If v = 10 V for the circuit of Figure 9, determine i1 , i2 and i3 . (b) Replace the resistors by a single resistor of equivalent resistance. 5. (a) Derive the mathematical model for the circuit of Figure 1 using i1 , i2 and i3 as outputs and v1 and v2 as inputs. (b) Draw a mechanical system analogous to the circuit. 6. (a) Derive the mathematical model for the circuit shown using i1 , i2 and i3 as outputs and v1 and v2 as inputs. (b) Draw a mechanical system analogous to the circuit.
1. (a) Derive a mathematical model for the mechanical system shown 4 using x1 , x2 , x3 and x4 as outputs and F1 and F2 as inputs. (b) Draw an electrical circuit analogous to this system.
1. Derive a mathematical model for the system of Figure 4 using x , the displacement of the mass center of the disk as the system output. Assume the disk rolls without slip. 2. Derive a mathematical model of the system of Figure 5 using x1 , x2 and x3 the displacements of the masses as the system outputs.

Wilkinson
School: University of Maryland

Attached.

System Dynamics

System Dynamics
Name of Student
Instituion Affiliation
Date

System Dynamics

Quiz5

Solution
Apply KVl AH loop (1)
L1 di/dt+Ri(i1-i2)+1/c i dt=v1
R1l1-R1l2+ l1di/dt+1/c i1dt=v1
Write in s domain:
R1i1(s)-R1i2(s) +l1si1+1/cs i1ls+v1(s)
I1(s)[R1+SL1+1/CS] –i2(s)R2=v1(s)
Apply KVL at loop 2
{L2di2/dt=R1(i2-i1)=1/c2)i2dt+ 1/c3(i2-i3)dt ...

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Anonymous
Awesome! Exactly what I wanted.

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