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19 Cards in this Set
- Front
- Back
What are the 2 formulas you need to know for Euler's formula?
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Δy = m*Δx
and y2 = y1 + Δy |
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When does Euler's method give an overestimate.
When does Euler's method give an underestimate. |
When f(x) is concave down.
When f(x) is concave up. |
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When n increases by a factor of p in Simpson's rule, what does the error decrease by?
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It decreases by a factor of p^4.
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Give the formulas for Newton's Law of Cooling
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dT/dt = -k(T-te)
T = Temperature of object te = temperature of the room T = ts - C*e^(-kt) ts = the starting tempertature of the object. C = ts - te |
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Name Kirchhoff's Laws:
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IR + L(dI/dt) = E
Ohms Henries Volts |
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Give Kirchhoff's Law for a capatictor:
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R(dQ/dt) + Q/C = E
Ohms 1/farads Volts |
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Give the Logistic Growth Pattern Formulas
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dP/dt = kP(1-P/K)
K = Carrying Capacity k = rate of change P = K/(1+Ae^(-kt)) A = K/Po - 1 |
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What equation do you use to figure out what case you're dealing with for Yc?
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sqrt(b^2 - 4ac)
> over = critical < under |
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How do you determine ά and β in the underdamped case?
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ά = -b/2a
β = sqrt(4ac-b^2)/2a |
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What is the formula for the underdamped case?
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e^(άx)*[C1*cos(βx)+C2*sin(βx)]
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When there is no damping or driving force, what is ω?
What is the formula for x(t) What is this case called? |
ω = squt(k/x)
x(t) = C1*sin(ωt) + C2*cos(ωt) Simple Harmonic Motion |
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How can x(t) = C1*sin(ωt) + cos*C2(ωt) be rewritten?
What does δ represent? |
??????????
x(t) = A(ωt + δ) A = amplitude = sqrt(C1^2 + C2^2) δ = the phase angle |
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What are the 2 formulas for δ in dealing with the simple harmonic motion?
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cos(δ) = -C1/A
sin(δ) = -C2/A |
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What is c?
What is k? |
c is the damping constant. Goes with y'.
k is the spring constant. Goes with y. |
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Write out the master SPRING formula
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m(d2x/d2t) + c(dx/dt) + ky = x(t)
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List Kirkarroff's differential formula.
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L(d2Q/dt2) + R(dQ/dt) + (1/C)Q = E(t)
Henries Ohms Ferads Volts |
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What is δ?
What is φ? |
δ is the phase angle.
φ is the phase shift. |
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Give the formulas for δ and φ involving sin and cos.
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sin(φ) = C1/A
cos(φ) = C2/A sin(φ) = -C2/A cos(φ) = -C1/A |
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Give the formula for frequency.
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f = ω/(2π)
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