A frictionless spring with a 4-kg mass can be held stretched 0.2 meters beyond its natural length by a force of 30 newtons. If the spring begins at its equilibrium position, but a push gives it an initial velocity of 1 m/sec, find the position of the mass after t seconds.

The position for mass is

Explanation:

Let x(t) donate the position of mass at time t,Then x satisfies the differential equation

The general solution is

It follows

thus the position of mass is

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explanation:

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