A frictionless spring with a 8-kg mass can be held stretched 2 meters beyond its natural length by a force of 40 newtons. If the spring begins at its equilibrium position, but a push gives it an initial velocity of 1.5 m/sec, find the position of the mass after t seconds.

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This question requires Hooke's law to solve:


where F is the force in newtons used to displace the mass by x in metres; k is the spring constant. With the force used to displace the mass, we can know the spring constant.


Using the fact that 


then it can be rearranged with Hooke's law to give


which can also be written as 


The solutions to this equations take the form




where A and B are the amplitudes (maximum displacement) of the system and `omega` is the angular frequency. As x(0)=0, the first of the two equations is appropriate in this occasion.

To determine the angular frequency we need the time period of the oscillator. This is 

(The entire section contains 2 answers and 402 words.)

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