A mass suspended from a spring oscillates in simple harmonic motion at a frequency of 4 cycles per second. The distance from the highest to the lowest point of the oscillation is 100 cm. Find an equation that describes the distance of the mass from its rest position as a function of time. Assume that the mass is at its lowest point when t = 0.

Explanation:

Given that,

Frequency of oscillation is

f = 4cycle per second

The distance from the highest to the lowest point of the oscillation is 100 cm

this is the distance from the minimum amplitude to the maximum amplitude i.e. 2A

Amplitude of oscillation

2A = 100cm = 1m

A = 1/2

A = 0.5m

An object position in simple harmonic motion (SHM) Is modelled generally as

y = A•Sin(wt)

Or

y = A•Cos(wt)

Since the amplitude is minimum at t=0

Then, the best modelled for this is

y = A•Cos(wt)

We know that, A= 0.5m

We know that,

w = 2πf

Then, w = 2π × 4

w = 8πrad/s

Then, the position of the mass at any time becomes

y = A•Cos(wt)

y = 0.5 • Cos(8πt)

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.

energy can be converted from one form to another, but it cannot be created or destroyed in ordinary chemical or physical means. do not understand what you are asking but hope this