Laplace Transform Question & Answers February 17, 2023 By Wat Electrical This article lists 100 Laplace transform MCQs for engineering students. All the Laplace transform Questions & Answers given below include a hint and a link wherever possible to the relevant topic. This is helpful for users who are preparing for their exams, or interviews, or professionals who would like to brush up on the fundamentals of Laplace transform. A Laplace transform is a mathematical form that converts real type variable function to complex type variable function. These functions are represented in the s-domain or a complex frequency-type domain. There is a number of conversion formulas in the Laplace transform where the integral of Laplace transform is L{f}(s) = Integration (0àinfinity) = f(t) e ^-st dt. Where f(t) is the time domain function, f(s) is the frequency domain function where “s” is given as sigma + jw. Laplace transform can be of different types such as bilateral Laplace transform, and Inverse Laplace transform. A Laplace transform where the limit values are extended on both sides is called a bilateral Laplace transform. A Laplace transform where the inverse operation is performed on the Laplace function is inverse Laplace function. Any function that involves in Laplace function deals with a probability value. The advantages of the Laplace transform include it represents ODE to simpler terms and changes the convolution type operators to multiplication operators. The disadvantages include it solves only known value constants and solving only complex equations and not simple ones. Laplace transform is used in fields such as optics, system modeling, and nuclear physics. 1).What is the linearity property of Laplace transform? A f1(t) + B f2(t) ⟷ A F1(s) + B F2(s) A f1(t) + B f2(t) ⟷ A F1(s) - B F2(s) A f1(t) + B f2(t) ⟷ A F1(s) * B F2(s) A f1(t) + B f2(t) ⟷ A F1(s) + B F2(s) A F1(s) Hint 2).What is the Frequency Shifting Property of Laplace Transform? es0t f(t)) ⟷ F(s - s0) es0t f(t)) ⟷ F(s + s0) es0t f(t)) ⟷ F(s * s0) es0t f(t)) ⟷ F(s0) Hint 3). What is the Integration of Laplace Transform? t∫0 f(λ) dλ ⟷ s F(s) t∫0 f(λ) dλ ⟷ F(s) t∫0 f(λ) dλ ⟷ 1⁄s F(s) Hint 4). What is the Multiplication by Time of Laplace Transform? T f(t) ⟷ (−d F(s)⁄ds) T f(t) ⟷ d F(s)⁄ds) T f(t) ⟷ F(s)⁄ds) T f(t) ⟷ (−t F(s)⁄ds) Hint 5). What is the Complex Shift Property of Laplace Transform? f(t) e−at ⟷ F(s + a) f(t) e−at ⟷ F(s - a) f(t) e−at ⟷ F(s * a) f(t) eat ⟷ F(s + a) Hint 6). What is the Time Reversal Property of Laplace Transform? f (-t) ⟷ F(-s) f (-t) ⟷ F(s) 0 1 Hint 7). What is the Time Scaling Property of Laplace Transform? f (t⁄a) ⟷ F(as) f (t⁄a) ⟷ s F(as) f (t⁄a) ⟷ a F(as) f (t⁄a) ⟷ s Hint 8). What is the standard notation of Laplace transform? L(f; s) = F(s) L(f; s) /F(s) L(f; s) * F(s) L(f; s) Hint 9). What is the Laplace Transform of 1 is? s o 1/s π Hint 10). What is the Laplace Transform of f'(t) is? sF(s) * f(0) sF(s) + f(0) sF(s) - f(0) F(0) Hint 11). What is the Laplace Transform of sin(at) is? as/(s2+a2) a/(s2+a2) s/(s2+a2) 1/(s2+a2) Hint 12). What is the Laplace Transform of t sin(at) is? as/(s2+a2)2 2as/(s2+a2) 2as/(s2+a2)2 as/(s2+a2) Hint 13). What is the Laplace Transform of sin(at +b) is? (s sin(b)+ a cos(b)/(s2+a2) (s sin(b)+ a cos(b) s/(s2+a2) (s sin(b)+ a cos(b)/(s+a) Hint 14). What is the Laplace Transform of sinh(at) is? 1/(s2-a2) 2a/(s2-a2) s/(s2-a2) a/(s2-a2) Hint 15). What is the Laplace Transform of eat sin(bt) is? 2b/((s-a)2+b2) b/((s-a)2+b2) ab/((s-a)2+b2) 1/((s-a)2+b2) Hint 16). What is the Laplace Transform of ect f(t) is? F(s+c) 1 F(s-c) 0 Hint 17). What is the Laplace Transform of eat is? 1/(s - a) 1/(s + a) 1/(s a) s/(a) Hint 18). What is the Laplace Transform of cos(at) is? as/(s2+a2) 2s/(s2+a2) a/(s2+a2) s/(s2+a2) Hint 19). What is the Laplace Transform of t cos(at) is? (s2+a2)/(s2+a2) (s2-a2)/(s2+a2)2 (s2+a2)/(s2-a2)2 (s2-a2)/(s2-a2) Hint 20). What is the Laplace Transform of cos(at + b) is? (s cos(b)+a sin(b)/(s2-a2) (s cos(b)-a sin(b)/(s2-a2) (s cos(b)+a sin(b)/(s2+a2) (s cos(b)-a sin(b)/(s2+a2) Hint 21). What is the Laplace Transform of cosh(at) is? 1/(s2-a2) s/(s2+a2) s/(s2-a2) a/(s2-a2) Hint 22). What is the Laplace Transform of e(at)cos((bt) is? (s+a)/((s-a)2+b2) (s-a)/((s-a)2-b2) (s+a)/((s-a)2-b2) (s-a)/((s-a)2+b2) Hint 23). What is the Laplace Transform of f’’(t) is? s2F(s) − sf(0) − f'(0) s2F(s) − sf(0) + f'(0) s2F(s) + sf(0) − f'(0) s2F(s)sf(0) − f'(0) Hint 24). What is the Laplace Transform of √(t) is? √π/2s(3.2) √π/2s(3/2) √π/2s(2) √π/2s(3) Hint 25). A two-sided Laplace transforms with extending limits of integrations is _______? Bilateral transform Inverse Laplace transform Laplace transform All the above Hint Laplace Transform MCQs for Exams 26). What is the Laplace transform of random variable X will be? L{f}(S) = E[e+sX] L{f}(S) = E[sX] L{f}(S) = E[e*sX] L{f}(S) = E[e-sX] Hint 27). Laplace Transform for simplifying the complicated differential equations by adding __________? Polynomials Random Variable Integers All The above Hint 28). Laplace transform is deployed in technical activities like? System Modelling Digital Signal Processing Electrical Circuit Analysis All The above Hint 29). Major application of Laplace transform is in_____? Telecommunications Signals Both a and b Motor Hint 30). What is the Inverse transform of the function F(s)? f(t) = 1/L+1{F(t)} f(t) = L-1{F(s)} f(s) = -L-1{F(s)} f(s) = 1/L-1{F(s)} Hint 31). If the two Laplace transform, say F(s) and G(s), then what will be the Inverse Laplace transform? L-1{aF(s)+bG(s)} = a L-1{F(s)} + bL-1 {G(s)} L-1{aF(s)+bG(s)} = a L-1{F(s)} + L-1 {G(s)} L-1{aF(s)+bG(s)} = a L-1{F(s)} - bL-1 {G(s)} L-1{aF(s)+bG(s)} = L-1{F(s)} - bL-1 {G(s)} Hint 32). What is the Inverse Laplace transform of 1 is ? 1/s s 0 1 Hint 33). What is the Laplace transform of sin(at)−at cos(at) is ? 2a3/(s2-a2)2 2a3/(s2+a2)2 2a3/(s2+a2) a3/(s2-a2)2 Hint 34). What is the Laplace transform of sin(at) + at cos(at) is ? 2as2/(s2+a2)2 2as2/(s2-a2)2 -2as/(s2+a2)2 as2/(s2+a2)2 Hint 35). What is the Laplace transform of cos(at)−at sin(at) is? (s2+a2)/(s2-a2)2 2s(s2−a2)/(s2+a2)2 (s2−a2)/(s2+a2)2 s(s2−a2)/(s2+a2)2 Hint 36). What is the Laplace transform of cos(at)−at sin(at) is? s(s2−3a2)/(s2+a2)2 s(s2+3a2)/(s2+a2)2 s(s2−2a2)/(s2+a2)2 s(s2-a2)/(s2+a2)2 Hint 37). What is the Laplace transform of eat sinh(bt)? b/(s−a)2 + b2 -b/(s−a)2 + b2 b/(s−a)2−b2 b/(s+a)2+b2 Hint 38). What is the Laplace transform of eat cosh(bt)? s-a/(s−a)2+b2 s-a/(s−a)2−b2 s+a/(s−a)2−b2 s-a/(s+a)2−b2 Hint 39). Laplace transform plays a important role in ? Control Systems Electrical Machines Switch Gear All the above Hint 40). What is the Integration of Laplace transform? t∫0 f(λ) dλ ⟷ 1⁄s t∫0 f(λ) dλ ⟷ 1⁄s F(s) t∫0 f(λ) dλ ⟷ F(s) t∫0 f(λ) dλ ⟷ s F(s) Hint 41). What is the Nth Derivative property of Laplace transform? (dn f(t)/ dtn) ⟷ sn F(s) − n∑i = 1 sn − i fi +1 (0−) (dn f(t)/ dtn) ⟷ sn F(s) − n∑i = 1 sn − i fi − 1 (0) (dn f(t)/ dtn) ⟷ sn F(s) − n∑i = 1 sn − i fi − 1 (0−) (dn f(t)/ dtn) ⟷ sn F(s) − n∑i = 1 sn + i fi − 1 (0) Hint 42). What is the Inverse Laplace transform of 1/s? 1 0 ∞ s Hint 43). What is the Inverse Laplace transform of 1/s , L-1(1/sn)? 1 tn/n!, n=1,2,3…. tn/(n+1)!, n=1,2,3,… tn/(n-1)!, n=1,2,3... Hint 44). What is the Inverse Laplace transform of (1/s2+a2)? sinat (1/a) sinat cosat 1 Hint 45). What is the Inverse Laplace transform of (1/s-a)? eat e-at et 0 Hint 46). What is the Inverse Laplace transform of (s/s2+a2)? cos at sin at cosec at sec at Hint 47). What is the Inverse Laplace transform of (1/(s-a)2+b2) b (1/b) eat sin bt b eat sin bt eat sin bt Hint 48). What is the Inverse Laplace transform of (s-a /(s-a)2+b2) eat eat sin bt cos bt eat cos bt Hint 49). Inverse Laplace transform is ____ type? Linear Non-Linear Constant Both a and b Hint 50). The Inverse Laplace transform of 1 is _____ type of function? Delta function Unit function Both a and b Star Hint Laplace Transform MCQs for Interviews 51). Laplace transform purpose is? To represent complex differential equation in to simple polynomial To convert derivate into a multiple domain variable To covert polynomials to differential equation using inverse Laplace transform All the above Hint 52). Laplace transform used in converting ____ functions? To convert time domain to frequency domain To convert frequency domain into time domain Both a and b To convert from frequency to mid frequency Hint 53). In which of the following field does laplace equation is used along with three-dimensional problem solving? Electrostatics Magnetostatics Moment Magento Force All the above Hint 54). In which of the following field laplace equation used along with 2D _______? Fluid Flow Electric Flow Ferromagnetic All The Above Hint 55). What is the Laplace transform of δ(t)? 0 1 2 ∞ Hint 56). Find the Laplace transform of e-at u(t) and its ROC? 1/(s-a) , Re{s}>a 1/(s+a) , Re{s}>-a (s+a) , Re{s}>a 1/(s-a) , Re{s}>-a Hint 57). Find the Laplace transform of u(t) and its ROC? . 1/s , σ<0 1/s , σ>0 1 s Hint 58). Find the inverse Laplace transform of F(s) = k/(s-a) (k and a are constants) is? k eat k/s eat s eat 1/s e Hint 59). Frequency domain is also called? S-domain P-domain S-plane Both a and c Hint 60). What is the Value of ∫_(-∞)^∞ [e^t Sin(t)]dt? 0.50 0.25 0.17 0.12 Hint 61). What is the value of ∫_(-∞)^∞[e^t log(1+t) ]dt? Sum of infinite integers Sum of infinite factorials 1 0 Hint 62). What is the Laplace transform of y(t) = e^t.t. Sint(t) cos(t)? (2(s+1))/[(s-1)^2+4]^2 (4(s-1))/[(s-1)^2+4]^2 (4(s+1))/[(s-1)^2+4]^2 (2(s-1))/[(s-1)^2+4]^2 Hint 63). What is the Laplace transform of L(cat) is ? 1/(s-2log(c)) 1/(s+2log(c)) 1/(2slog(c)) -1/(s+2log(c)) Hint 64). What is the Laplace transform of d/(dt ) (sint/t)? s×cot-1 s-1 s×tan-1 s-1 s×sin-1 s-1 s×cos-1 s-1 Hint 65). What is the Laplace transform of (sinh(at))/(t )? 1/(3 ) 1/(2 ) log( (s-a)/(s+a)) 1/(2 ) log( (s-a)/(s+a)) 1/(3 ) 1/(2 ) log( sa/(s+a)) 1/(2 ) log( (s+a)/(s-a)) Hint 66). What is the mathematical representation of Inverse Laplace transform is _________? f(t)=L-1{F(s)} f(t)=L-1{F(x)} f(t)=L-1{F(t)} f(s)=L-1{F(t)} Hint 67). A system is said to be stable if ? Poles lies at the left of the imaginary axis Poles lies at the right of imaginary axis Zeros lies at the left of the imaginary axis Zeros lies at the right of the imaginary axis Hint 68). What is the Initial value theorem? lim┬(t→0^+ )〖x(t)〗 = lim┬(s→infinite)s x(s) lim┬(t→0^+ )〖x(t)〗 = x(s) lim┬(t→0^+ )〖x(t)〗 = lim┬(s→0)s x(s) lim┬(t→0^- )〖x(t)〗 = lim┬(s→0)s x(s) Hint 69). If x(t) =δ(t) then Laplace transform of X(S) and Roc ? δ(t)1 and Roc is imaginary axis δ(t)1 and Roc is imaginary axis δ(t)1 and Roc is infinite δ(t)1 and Roc is zero Hint 70). If Laplace transform of x(s) is rational then ROC? ROC does not contain any pole ROC does contain pole ROC is infinite All the above Hint 71). If x(t) is Right sided signal then ROC of its Laplace transform of X(s) will be? Right to the Right most of pole Left side of pole Imaginary axis Left to the Left most pole in S-plane Hint 72). If x(t) is Right sided signal then ROC of its Laplace transform of X(s) will be? Right to the Right most of pole Left side of pole Imaginary axis Left to the Left most pole in S-plane Hint 73). If x(t) is Double sided signal then ROC of its Laplace transform of X(s) will be ? Right to the Right most of pole Between the poles but does not contain any pole Imaginary axis Left to the Left most pole in S-plane Hint 74). Frequency domain involves in? Maths Signals Physics Both a and b Hint 75). What is the Laplace transform of the signal x(t) = (dδ(t))/dt? 1 0 s 1/s Hint Laplace Transform MCQs for Students 76). What is the Laplace transform of x(t) = 1/(√Πt)? S ^-1⁄2 S^-1 S^-2 S^1⁄2 Hint 77). Frequency is expressed as ? Hertz Seconds Ohms Watts Hint 78). Which of the following is the advantage of frequency domain? Solves linear differential equation Converts in to other domain Solves complex equations All the above Hint 79). What is The Unilateral Laplace transform? Different inputs and Same output Same inputs and Different outputs Same inputs and Same outputs Different inputs and Different outputs Hint 80). What is The Bilateral Laplace transform? Different inputs and same output Same inputs and different outputs Same inputs and Same outputs Different inputs and different outputs Hint 81). What is Laplace transform? A mathematical method for solving differential equations A technique for finding the frequency response of a system A method for solving integral equations A technique for solving partial differential equations Hint 82). What is the Laplace transform of the unit step function? 1/s 1-e^(-s) s 1/s^2 Hint 83). What is the inverse Laplace transform of 1/s^2? t t^2 1 e^-t Hint 84). What is the Laplace transform of e^(-at)u(t)? 1/(s+a) e^(-as) s/(s+a) a/(s+a) Hint 85).What is the Laplace transform of a periodic function? Converges to a complex function Converges to a real function Does not converge Converges to a constant function Hint 86). What is the Laplace transform of a impulse function? Converges to 1 Converges to 0 Converges to a complex function Does not converge Hint 87). Laplace transform can be used for what kind of equation? Linear differential equation Nonlinear differential equation Linear algebraic equation All of the above Hint 88). What is the Laplace transform of a derivative of a function? sL(x(t)) - x(0) L(x'(t)) L(x(t))/s -L(x(t))/s Hint 89). What is the Laplace transform of a integral of a function? L(∫x(t)dt) 1/s L(x(t)) L(x(t))/s -L(x(t))/s Hint 90). What is the Laplace transform of a convolution of two functions? L(x(t))*L(y(t)) L(x(t)y(t)) L(x(t))+L(y(t)) L(x(t))/L(y(t)) Hint 91). What is the Laplace transform of a cosine function? (s^2 + 1)/(s^2 + 2s cos(w)+ 1) (s^2 + 1)/(s^2 + 2s + 1) (s^2 + 1)/(s^2 - 2s cos(w) + 1) (s^2 + 1)/(s^2 - 2s + 1) Hint 92). What is the Laplace transform of a sine function? (s^2 - 1)/(s^2 + 2s sin(w) + 1) (s^2 - 1)/(s^2 + 2s + 1) (s^2 - 1)/(s^2 - 2s sin(w) + 1) (s^2 - 1)/(s^2 - 2s + 1) Hint 93).What is the Laplace transform of a impulse function? 1/s^2 1/s 1 0 Hint 94).What is the Laplace transform of a function that is zero for tT? (1 - e^(-sT))/s e^(-sT) 1 - e^(-sT) 1 - e^(-sT))/s^2 Hint 95). What is the Laplace transform of a function that is zero for t>T? (1 - e^(-sT))/s e^(-sT) 1 - e^(-sT) 1 +e^(-sT) Hint 96). What is the Laplace transform of a function that is zero for t<T? e^(-sT) (1 - e^(-sT))/s 1 - e^(-sT) (1 - e^(-sT))/s^2 Hint 97). What is the Laplace transform of a function that is zero for t<0? 1/s 1 e^(-sT) 0 Hint 98). What is the Laplace transform of a function that is zero for t>0? 1/s 1 e^(-sT) 0 Hint 99). What is the Laplace transform of a function that is zero for t≠0? 1/s 1 e^(-sT) 0 Hint 100). What is the Laplace transform of a function that is zero for t=0? 1/s 1 e^(-sT) 0 Hint Time's up