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2 years ago

find a model for simple harmonic motion if the position at t=0 is 0 the amplitude is 5 centimeters and the period is 4 seconds

Mathematics

2 answers:

Alexeev081 [22]2 years ago

7 0

Answer:

y = 5sin $(\frac{x}{2})$

Step-by-step explanation:

Since harmonic motion is represented by the sine wave equation.

y = a sin (bx)

where a = amplitude

period = $\frac{2\pi}{b}$

Amplitude of the harmonic motion is given as 5 and period is 4 seconds.

so a = 5

and 4 = $\frac{2\pi}{b}$ ⇒ b = $\frac{2\pi}{4}$

b = $\frac{\pi}{2}$

Now we replace the values of a and b in the sine equation

y = 5sin $(\frac{x}{2})$

Jobisdone [24]2 years ago

6 0

<span>d = 5sin(πt)
hope this helped</span>

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2 years ago

Zac and Lynn are each traveling on a trip. So far, Zac has traveled 123.75 miles in 2.25 hours. Lynn leaves half an hour after Z

Savatey [412]

Complete question is;

Zac and Lynn are each traveling on a trip. So far, Zac has traveled 123.75 miles in 2.25 hours. Lynn leaves half an hour after Zac. So far

she has traveled 105 miles in 1.75 hours. Assume Zac and Lynn travel at constant rates.

Let a represent the number of hours that have elapsed since Zac started traveling. Let y represent the number of miles traveled. Write a system of linear equations that represents the distance each of them has traveled since Zac left on his trip.

Assume Zac and Lynn continue to travel at the same constant rates and make no stops.

Determine the solution of the system of linear equations.

Answer:

Zac: y = 55a

Lynn: y = 60(a - ½)

6 hours after Zac started traveling, both Zac and Lynn would have covered 330 miles each.

Step-by-step explanation:

Zac has traveled 123.75 miles in 2.25 hours. Since he travels at constant speed, we can say;

zac's speed = 123.75/2.25 = 55 mi/hr

Similarly, Lynn traveled 105 miles in 1.75 hours. Thus, since she travels at a constant speed;

Lynn's speed = 105/1.75 = 60 mi/hr

Now, we are told that a represents the number of hours that have elapsed since Zac started traveling and y represents the number of miles traveled.

Thus;

a hours after Zac started travelling, his distance covered will be;

Zac: y = 55a

Now,for Lynn, since she started ½ an hour after Zac, it means a hours after Zac started, she had traveled (a - ½) hours.

Thus, Lynn's distance traveled after Zac started = 60(a - ½)

Lynn: y = 60(a - ½)

The solution will be when they have travelled equal distances a hours after Zac started. Thus;

55a = 60(a - ½)

55a = 60a - 30

60a - 55a = 30

5a = 30

a = 30/5

a = 6 hours

Putting 6 for a in y = 55a, we have;

y = 55 × 6

y = 330 miles

5 0

2 years ago

When Θ = 5 pi over 6, what are the reference angle and the sign values for sine, cosine, and tangent?

stira [4]

Note that (5π)/6 radians = 150°. Therefore the given angle is in quadrant 2.

Refer to the figure shown below.

Reference angles are measured relative to the horizontal axis.
Therefore the reference angle in each quadrant is π/6 radians or 30°.
Denote the reference angle as θ'.
Then, in quadrant 1,
cos θ' = √3/2, sin θ' = 1/2, tan θ' = √3.

Because we are in quadrant 2,
sin θ' = π/6;
sin(5π/6) is positive, but cos (5π/6) and tan (5π/6) are negative.

Answer:
5π/6 is in quadrant 2.
The reference angle, θ' = π/6.
sin(5π/6) is positive, cosine and tangent are negative.