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I´ve got problems with solving this task! Please help me with the solutions. Maybe someone knows how it works. I solved it from 1-4 and don´t know 5-8

Thanks

Tim

The Crank - rocker consists of rocker 1, coupler 2 and rocker 4. It´s connected with swivel joints. The rack is fixed.

We look at the point mass m in A and the torsion spring (with damper) in B0. The weight and the inert force because of the motion affect in A (vx,vy ax,ay). All other components are without mass, rotary inertia could also been disregarded.

For the "Resetmoment" in B0:

Mc = cT*(psi-psic0) + dT*dpsi/dt

against the rotation

For psi stands:

psi = Pi-arctan(a*sin(phi), d-a*cos(phi))

arccos((1/2)*(d^2-2*d*a*cos(phi)+a^2+b^2-c^2)/(b*sqrt(d^2-2*d*a*cos(phi)+a^2)))

From the position of A:

location:

rx = a cos(phi), ry = a sin(phi)

speed:

drx/dphi = rx1 (y appropriate)

acceleration

drx1/dphi = rx2 (y appropriate)

angle speed:

dphi/dt = phip "(phi)point"

angle acceleration:

d(phip)/dt = phipp "(phi)pointpoint"

With this expressions stands:

vx = rx1*phip, vy = ry1*phip, ax = rx1*phipp + rx2*phip^2, ay = ry1*phipp + ry2*phip^2

and we write the balance of the virtual performance

-m*ax*rx1 - m*ay*ry1 - m*g*ry1 - ( cT*(psi-psic0) + dT*psi1*phi_p ) * psi1 = 0

TASK DESCRIPTION:

1. Differentiate the position/speed and Acceleration and write the equation of the acceleration. Set the paramter

{ a = 0.2 (m), b = 0.3, c = 0.4, d = 0.4, g = 9.81 (m/s^2), m = 1.3 (kg), cT = 2 (Nm/rad), dT = 0.4 (Nms/rad), psic0 = Pi/2 (rad) }

2. Set up the differential equation (DGL) in phi

3. Set up the equation of the static balance and find out a realistic stable layer.

Set phi_stat=? and psi_stat in rad and degree! Hint: Plot the function to find the solution

4. Linearize the differential equation (DGL) around the static balance (phi=phi_stat + Delta) for little oscillations around this balance position.

Express the Differential equation only with delta

5. Identify the balance position out of this DGL angular frequency omega_0 of the undamped system

6. Calculate the own frequency (?) f in Hz of the undamped system and the "degree of dumping" theta (without dimension). (f=0.93965Hz)

7 . For a sinoid acceleration stimulation around the Axis A0 set and plot the frequency response for oscillations around the static balance position. mark the own-frequency omega_0.

8. Calclate the amplitude in [dB] for omega --> and omega = omega_0