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PRACTICE PROBLEMS

1. Given the following transfer function perform the following operations.

a) Draw a Bode plot using the straight line methods (using the graph paper on the next page).

b) Determine y(t) if x(t) = 20 + 3 sin(10t) using the Bode plot.

c) Determine y(t) if x(t) = 20 + 3 sin(10t) using phasors.

2. Draw a Bode Plot for both of the transfer functions below using the phasor transform.

3. Given the transfer function below,

a) draw the straight line approximation of the Bode (gain and phase shift) plots.

b) determine the steady-state output if the input is x(t) = 20 sin(9t+0.3) using the Bode plot.

4. Use the straightline approximation techniques to draw the Bode plot for the transfer function below.

5. Given the transfer function below,

a) Find the steady state response of the circuit using phasors (i.e., phasor transforms) if the input is Vi=5sin(100,000t).

b) Draw an approximate Bode plot for the circuit.

6. For the transfer function,

a) Use the straight line method and the attached log paper to draw an approximate Bode plot.

b) Verify the Bode plot by calculating values at a few points.

c) Use the Bode plot to find the response to an input of 5sin(624t) + 1sin(6.2t).

7. The applied force ‘F’ is the input to the system, and the output is the displacement ‘x’. Neglect the effects of gravity.

b) What is the steady-state response for an applied force F(t) = 10cos(t + 1) N ?

c) Give the transfer function if ‘x’ is the input.

d) Draw the bode plots for the transfer function found in a).

e) Find x(t), given F(t) = 10N for t >= 0 seconds.

f) Find x(t), given F(t) = 10N for t >= 0 seconds considering the effects of gravity.

8. The following differential equation is supplied, with initial conditions.

a) Write the equation in state variable form.

b) Solve the differential equation numerically.

c) Solve the differential equation using calculus techniques.

d) Find the frequency response (gain and phase) for the transfer function using the phasor transform. Sketch the bode plots.

9. You are given the following differential equation for a spring damper pair.

a) Write the transfer function for the differential equation if the input is F.

b) Apply the phasor transform to the transfer function to find magnitude and phase as functions of frequency.

c) Draw a Bode plot for the system using either approximate or exact techniques.

d) Use the Bode plot to find the response to;

e) Put the differential equation in state variable form and use a calculator to find values in time for the given input.

f) Give the expected ‘x’ response of this first-order system to a step function input for force F = 1N for t > 0 if the system starts at rest. Hint: Use the canonical form.

10. Given the frequency response plot below, develop a transfer function.

11. For the transfer function below drawn an approximate bode plot. Use the approximate Bode plot to estimate the response to the input. Verify the results using phasors.