A. What is the equation describing the motion of a mass on the end of a spring which is stretched 8.8cm from equilibrium and then released from rest, and whose period is 0.66s? Assume that the displacement at the start of the motion is positive. (express your answer in terms of t using two significant figures.)

B. What will be its displacement after 1.7s? (express your answer to two significant figures and include the appropriate units.)

(a)      

(b)  and after 1.7s the displacement would be

Explanation:

This is periodic motion and the best equation to model this type of motion is sinusoidal equation.

We will chose cos function because it starts at the max or the amplitude.

A = 8.8cm, T = 0.66s in following general form gives the answer.

and substituting t = 1.7s in it gives us 8.456461cm, just little bit lower than initial position.

answer: at 24 february, 2014 the population gets twice of its initial population.

explanation:

since we have given that

the population for alpha city, t years after january 1, 2004 is given as

first we find out the initial population, i.e. t=0,

so, our quadratic equation becomes,

according to question, we have said that if the population has twice its initial population, then it becomes

so, time taken to reach this above mentioned population is given by

now, we know that time can't be negative so, we take t=9.149 years.

hence, at 24 february, 2014 the population gets twice of its initial population.

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