A type of cuckoo clock keeps time by having a mass bouncing on a spring, usually something cute like a cherub in a chair. What force constant is needed to produce a period of 0.500 s for a 0.0150-kg mass

the force constant  k = 2.369 N/m

Explanation:

Given that:

A type of cuckoo clock keeps time by having a mass bouncing on a spring, usually something cute like a cherub in a chair.

with period T = 0.500 s and a mass of 0.0150 kg, Then the force constant can be calculated by using the formula:

where;

T = time period

m = mass

k = force constant.

By making k the subject of the formula; we have:

replacing our given values , we have:

k = 2.369 N/m

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.