A mass hanging from a vertical spring is in simple harmonic motion as given by the following position function, where t is measured in seconds and s is in inches: s(t)=−3cos(πt+π4). Determine the position of the spring at t=1.5 s. Find the velocity of the spring at t=1.5 s.

The position and velocity of the spring is −2.12 inches and -6.66 ft/s.

Explanation:

Given that,

The position function,

We need to calculate the position of the spring at t = 1.5 s

Using position function

Put the value of t in the function

We need to calculate the velocity of the spring

Using position function

On differentiating

Put the value into the formula

Hence, The position and velocity of the spring is −2.12 inches and -6.66 ft/s.

the simple machine has three main features. they are:

fulcrum is the center point or pivot point of the machine. effort is input force/ applied force. load is external force/ output.

the keisha 's machine labels are

x : load

y: fulcrum

z: lever

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.