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Question

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 C 4s2+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.04+F(s)=0
F(s)=4s2+1, the laplace transform of f(t).

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