A15 kilogram object is suspended from the end of a vertically hanging spring stretches the spring 1/3 meters. at time t = 0, the resulting undamped mass-spring system is disturbed from its rest state by the force f(t) = 170 cos(5t) and no initial velocity. the force f(t) is expressed in newtons (am) and time is measured in seconds. what initial value problem models this situation?

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Step-by-step explanation:

See the attached image

This problem involves Newton's 2nd Law which is: ∑F = ma, we have that the acting forces on the mass-spring system are: that correspond to the force of resistance on the mass by the action of the spring and that is an external force with unknown direction (that does not specify in the enounce).

For determinate we can use Hooke's Law given by the formula where correspond to the elastic constant of the spring and correspond to  the relative displacement of the mass-spring system with respect of his rest state.

We know from the problem that an 15 Kg mass stretches the spring 1/3 m so we apply Hooke's law and obtain that...

Now we apply Newton's 2nd Law and obtaint that...

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Finally... ±

We know from the problem that there's not initial displacement and initial velocity, so... and

Finally the Initial Value Problem that models the situation describe by the problem is

answer: 2 litters juice bottle

half of a gallon is 50% of a full gallon 2 litters of juice is 52% of a full gallon

hope this ^_^