The function f(t) satisfies the differential equationd2fdt2+f=0 and the auxiliary conditions, f(0)=0,dfdt(0)=4. The Laplace transform of f(t) is given by
A
2s+1
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B
4s+1
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C
4s2+1
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D
2s4+1
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Solution
The correct option is C4s2+1 Given differential equation is d2fdt2+f=0...(1)
Also f(0)=0,dfdt(0)=4
Taking laplace transform of equation (1), we get ⇒L[d2fdt2+f]=0 ⇒s2F(s)−s.0−4+F(s)=0 ⇒F(s)=4s2+1, the laplace transform of f(t).