# If the acceleration of the mass of a spring mass system is equal to $2 \sin 5t,$ the resulting motion is

a.       A SHM with zero mean displacement b.      Combination of SHM and linear motion  c.       A SHM with the mean displacement of 1 unit d.      The mass does not move.

## 1 Answer

We integrate acceleration to get velocity and integrate velocity to get position.
Taking the initial values of their integrals (definite integrals) we see that velocity is $\large\frac{2}{2}$$(\cos 2 t) with initial velocity as zero and the position is (t- \large\frac{1}{2}$$\sin 2t)$ and thus the position keeps increasing with time while it has an oscillating component $-\large\frac{1}{2}$$\sin 2t$ and thus 'b' is correct answer
Hence b is the correct answer.
answered Dec 11, 2013 by

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