When a spring with spring constant k is cut into three equal parts the force constant of each of the part would be?

177.

The displacement x of a particle varies with time t as, x = ae-αt +b e βt where a, b α and β are positive constants. The velocity of the particle will

• go on decreasing with time

• be independent of α and β

• drop to zero when α = β

• go on increasing with time

D.

go on increasing with time

x = a e αt +b e βtSo velocity  v = dXdt   =-a αe-αt + b βe βeν = A + BWhere A = -a αe-αt , B =b βe βr

The value of term A = a e-αt decreases and of term B = b βeβe increases with increase in time. As a result, velocity goes on increasing with time.

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