Labs: Resonance and Skin Impedance

Question 1

How can mass be converted into force in newtons?

Answer 1

multiply mass in kg by 9.8 m/s²

Question 2

What graphs were done for the resonance lab?

Answer 2

1. force (x) vs. displacement (y) … a linear relationship
2. frequency (x) vs. displacement (y) … a graph with a peak at the resonant frequency

Question 3

How is the spring constant determined from the graph of force vs. displacement?

Answer 3

the slope is the spring constant because

F = -k * x

can be equated to

Y = mx + b

with b = 0 b/c with zero force there’s zero displacement

Question 4

What are the 3 types of oscillation discussed in the resonance lab manual?

Answer 4

Undamped Free Oscillation: harmonic oscillation unaffected by damping factors (friction)

Damped Free Oscillation: harmonic oscillation affected by damping factors

Damped Driven Oscillation: harmonic oscillation with an external force counteracting the damping factors in which the external force’s frequency eventually becomes the oscillatory system’s frequency

Question 5

What is critical damping?

Answer 5

damping that causes an energy loss per period which keeps the system from reaching equilibrium before passing through it

Question 6

What is eigenfrequency?

Answer 6

the characteristic frequency at which an oscillatory system oscillates

Question 7

What was done in the resonance lab?

Answer 7

• the relationship between force and displacement of a cantilever was measured
• the phenomenon of eigenfrequency was observed by driving the oscillation of the cantilever at different frequencies until the one with the highest displacement was found

Question 8

What is Ohm’s Law for DC current?

For AC?

Answer 8

for DC: U = I * R

U is voltage

I is current (amperes)

R is resistance (Ohms)

for AC: U_rms = I_rms * Z_rms

rms is root-mean-square

z is impedance (Ohms)

Question 9

In direct current measurements, where does current not flow?

And how does this effect the circuit diagram?

Answer 9

through capacitors

so they can be neglected

Question 10

Why can the resistance of the auxiliary electrode and muscle be ignored?

Answer 10

because they are so small compared to the resistance of the measuring electrode

• auxiliary electrode is large and therefore low resistance
• muscle is rich in electrolytes and therefore also low resistance

Question 11

What is the formula for specific resistance?

In what case is it used?

Answer 11

ρ* = R x A

ρ* = specific resistance (Ohms * m²)

R = resistance

A = surface area of measuring electrode

• used for direct current

Question 12

What is the formula for specific capacitance?

In what case is it used?

Answer 12

γ* = C/A

γ* is spec. capacitance (Farad/m²)

C is capacitance

A is surface area of measuring electrode

• used with alternating current

Question 13

In alternating current measurements of sufficient frequency, what parts of the circuit diagram can be neglected?

Answer 13

resistances

Question 14

How can root mean square values be calculated from normal values?

Answer 14

multiply by 0.707

Question 15

What is the formula for capacitance?

Answer 15

C = 1 / (2π * f * Z)

f = frequency

Z = impedance

Question 16

How is specific resistance found if given a (DC) voltage and current?

Answer 16

1. Use U = R * I to get resistance (R)
2. Use **ρ* = R x A **to get specific resistance

Question 17

How is specific capacitance found if given a voltage (AC), frequency and current?

Answer 17

1. Convert the voltage (U) to root-mean-square voltage (U_rms) by multiplying by 0.707
2. Use U_rms and current to get impedance (Z) via the equation: Z = U_rms/I_rms
3. Use impedance and frequency to get capacitance via the equation: C = 1 / (2π * f * Z)
4. Use capacitance and electrode surface area to get specific capacitance via the equation: γ* = C/A