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Differential Equations

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Question 1

A particle moves on the x-axis with an acceleration , a=(6t-4)ms^-2 . Find the position and velocity of the particle at t=3 , if the particle is at origin and has a velocity of 10ms^-1 when t=0 by using either the method of undetermined coefficient or Laplace Transform .

Question 2

The series circuit consists of an electromotive force which is supplied by a battery 12-V, a resistor with R=20ohm , an inductor with L=1H , and a capacitor with C=0.002F . Given
that the current , I is the rate of change of the capacitor Q with respect to t . It is known that
the voltage drops across the resistor, capacitor and inductor are RI , Q/C and L dI/dT respectively. By using Kirchhoff’s voltage law L dI/dT + RI + Q/C = E(t) where E(t) s the
supplied voltage and the initial charge and current are both 0, determine :

a) The charge , Q at the time , t .

b) The charge , Q at the time , t if the battery is replaced by a generator producing a voltage of E(t)=12sin10t

Please help me to solve this equation...

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