Tuesday

September 30, 2014

September 30, 2014

Posted by **COFFEE** on Tuesday, July 10, 2007 at 8:05pm.

----------------------

Q" + 24 Q' + 200 Q = 12 sin (10t)

r^2 + 24r + 200 = 0

r = -12 +/- 2sqrt(14)*i

Qc(t) = e^-12*(c1*cos(2sqrt(14)t)+c2*sin(2sqrt(14)t))

Qp(t) = A*cos(10t) + B*sin(10t)

Q'p(t) = -10A*sin(10t) + 10B*cos(10t)

Q"p(t) = -100A*cos(10t) - 100B*sin(10t)

(-100A*cos(10t)-100B*sin(10t))+24(-10A*sin(10t)+10B*cos(10t))+200(A*cos(10t)+B*sin(10t))

(100A+240B)*cos(10t)+(100B+240A)*sin(10t)=12*sin(10t)

100A+240B=12 -> 25A + 60B = 3

-240A+100B=0 -> -48A + 20B = 0

B = 36/845, A = 3/169

Q(t)=e^(-12t)(c1*cos(2sqrt(14)t)+c2*sin(2sqrt(14)t))+(3/169)cos(10t)+(36/845)sin(10t)

c1 = -3/169

I(t)=e^(-12t)[(-12*c1+2sqrt(14)*c2)cos(2sqrt(14)t)+(-2sqrt(14)*c1-12*c2)sin(2sqrt(14)t))]

+(10/845)(15*cos(10t)+36*cos(10t))

I(0)=-12*c1+2sqrt(14)*c2+(360/845)=0

c2 = 108/(338sqrt(14))

Q(t)=e^(-12t)((-3/169)cos(2sqrt(14)t)+(108/(338sqrt(14))sin(2sqrt(14))+(1/845)(15cos(10t)+36sin(10t))

Also,

I(t)=e^(-12t)[(144/169)cos(2sqrt(14)t)-(1128/(338sqrt(14))sin(2sqrt(14)t)]

Is this correct? Thanks.

Substitute Q(t) in the differential equation to see if it is correct. The probability of making two mistakes that exactly cancel each other out is pretty small...

Ok, its incorrect. Where am I making a mistake?

Check if Qp satisfies the inhomogeneous equation and if Qc satisfies the homogeneous part.

**Answer this Question**

**Related Questions**

Physics - In a series circuit, a generator (1400 Hz, 12.0 V) is connected to a ...

Physics - In a series circuit, a generator (1400 Hz, 12.0 V) is connected to a ...

physics please help!! - 1. A 26.0-Ω resistor, a 12.0-µF capacitor, and a 17...

physics - In a series circuit, a generator (1254 Hz, 13.8 V) is connected to a ...

physics - often it is highly desirable to minimize the impedance in a circuit. ...

Differential Equations - Question 1 A particle moves on the x-axis with an ...

Math/Calculus - A series circuit contains a resistor with R = 24 ohms, an ...

Physics - A circuit contains a self-inductance L in series with a capacitor C ...

Physics - A 50 ohm resistor is connected in series with a 0.2 H inductor, a 40 ...

Physics - A series circuit contains only a resistor and an inductor. The voltage...