    Question

# The relationship between the force f(t) and the displacement x(t) of a spring-mass system with a mass M, viscous damping D and spring constant K, Md2x(t)dt2+Ddx(t)dt+Kx(t)=f(t) X(s) and F(s) are the Laplace transforms of x(t) and f(t) respectively. With M= 0.1, D = 2, K= 10 in appropriate units, the transfer function G(s)=X(s)F(s) is

A
10s2+20s+100
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B
s2+20s+100
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C
10s2s2+20s+100
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D
ss2+20s+100
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Solution

## The correct option is A 10s2+20s+100Md2x(t)dt2+Ddx(t)dt+Kx(t)=f(t) Taking Laplace transform on both sides, Ms2 X(s)+Ds X(s)+K X(s)=F(s) X(s)F(s)=1Ms2+DS+K By substituting, M, D and K values, X(s)F(s)=10.1s2+2s+10 =10s2+20s+100  Suggest Corrections  0      Similar questions
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