CHAPTER – 1 – LAPLACE TRANSFORM.
2 Marks :
(5 two marks will be asked from this model)
1 .Define Laplace
Transform .
2. State the condition for the existence of Laplace Transform.
3. Define the Laplace transform of Unit step Function.
4. Define the Laplace transform of Unit Impulse Function.
5. State Linear Property of Laplace Transform. *
6. State First Shifting Property of Laplace Transform. *
7. State Second Shifting Property of Laplace Transform. *
8. State Convolution theorem of Laplace Transform.
9. State Initial & Final value theorem of Laplace Transform. *
10. Define Laplace transform of derivatives. *
11. Define the Laplace transform of Integration. *
12. Two Marks Problem Using * (above star ‘ ed ) theorem & Property.
13. Simple Problem Using Laplace Transform & Inverse Laplace
Transform.
14. Find the Laplace transforms of
(a) sin 2t sin 3t
(b) cos2 2t
(c) sin3 2t
(d) e−3t2 cos 5t − 3 sin 5t
(e) e3t sin2
t
(f) t cos at
(g) t2 sin at
(h) 1−et
t
(i) t3e−3t
(j) te−t sin 3t
(k) sin kt − kt cos kt
(l) sin at
t
(m) sin2
t
15.
Write a function for which Laplace
transformation does not exist. Explain why Laplace transform does not exist.
16. If L(f(t)) = F(s)
what is L(e-atf(t))?
17. Find the Laplace
transform of e-2t (1+t)2.
18. Find the Laplace
transform of te-t sint.
19. Find L(tsin2t).
20. Obtain the
Laplace transform of sin2t-2tcos2t in the simplified form.
21. Verify the
initial value theorem for f(t) = 5 + 4cos2t.
22.Find the
Laplace transform of t coshat.
23.Find
the Laplace Transform of unit step function at t=a. 24.Does the Laplace
transform of Cos a t/ t exist? Justify.
25.Find
L-1 {( cot-1 (s) }
15 marks :
(You can Omit Atmost one Part Mentioned Below)
PART 1 – FIND THE
LAPLACE TRANSFORM.
PART 2 – FIND THE LAPLACE INVERSE.
PART 3 – LAPLACE TRANSFORM OF PERIODIC FUNCTIONS.
PART 4- LAPLACE INVERSE USING CONVOLUTION THEOREM.
PART 5 – APPLICATION TYPE ( LAPLACE TRANSFORM OF DIFFERENTIATION &
INTEGRATION i.e SOLVE TYPE SUM)
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