Category solved model papers

Obtain half-range sine series for

Obtain half-range sine series forf(x)= 𝑘𝑥 , 0 ≤ 𝑥 ≤ 𝑙/2 𝑘(𝑙 − 𝑥) , 𝑙/2≤ 𝑥 ≤ 𝑙 Answer:-

Find the Fourier series expansion of 𝑓(𝑥) = 2𝑥 − 𝑥² , 𝑖𝑛 ( 0, 3)

Find the Fourier series expansion of 𝑓(𝑥) = 2𝑥 − 𝑥2 , 𝑖𝑛 ( 0, 3) Answer:-

Show that there is a direct current part of 0.75 amp in the variable current and obtain the amplitude of the first harmonic.

The following table gives the variation of periodic current over a period. t sec 0 T/6 T/3 T/2 2T/3 5T/6 T A amp 1.98 1.30 1.05 1.30 -0.88 -0.25 1098…

Obtain the half-range cosine series for 𝑓(𝑥) = 𝑥 𝑠𝑖𝑛𝑥 in (0, 𝜋) and hence show that

Obtain the half-range cosine series for 𝑓(𝑥) = 𝑥 𝑠𝑖𝑛𝑥 in (0, 𝜋) and hence show that − ⋯ ∞ Answer:-

Find a Fourier series to represent 𝑓(𝑥) = 𝑥² 𝑖𝑛 − 𝜋 ≤ 𝑥 ≤ 𝜋

Find a Fourier series to represent 𝑓(𝑥) = 𝑥2 𝑖𝑛 − 𝜋 ≤ 𝑥 ≤ 𝜋 Answer:-

Solve by using Laplace transform techniques

Solve by using Laplace transform techniques with x(0)=2 and x'(0)=-1 Answer:-

Find the inverse Laplace transform of

Find the inverse Laplace transform of Answer:-

Using the unit step function, find the Laplace transform of

Using the unit step function, find the Laplace transform off(t)= cos𝑡, 0 ≤ 𝑡 ≤ 𝜋cos2𝑡 , 𝜋 ≤ 𝑡 ≤ 2𝜋cos3𝑡 , 𝑡 ≥ 2𝜋 Answer:-

Using the convolution theorem find the inverse Laplace transform

Using the convolution theorem find the inverse Laplace transform of Answer:-

Find the Laplace transform of the square–wave function of period a given by

Find the Laplace transform of the square–wave function of period a given byf(t)= 1, 0<t<a/2-1, a/2<t<2 Answer:-