answersLogoWhite

0


Best Answer

I'm not entirely sure about this, but imagine that you have a coordinate system where the x-axis is in units of seconds (variable name t) and the y-axis is in units of centimeters (variable name d (for displacement)). Simple harmonic motion would indicate a simple periodic motion pattern, which would hint at a sine or cosine function. Using the above coordinate system, an unmodified cosine wave would have an amplitude of 1.0 cm and a period of 2(pi) seconds:

d=cos(t)

I chose cosine because cosine at t=0 (x=0) would be at whatever its amplitude is.

To get the amplitude to be 2.0 cm is easy, you must simply modify the amplitude of the cosine function by multiplying it by 2. So far:

d=2cos(t)

To modify the period to fit the problem statement, you must start with the fact that an unmodified cosine function would have a period of 2(pi). If you were to cut the period in half, you would multiply the argument inside the function by 2, which would give it a period of (pi). This would look like:

y=cos(2x)

So, if multiplying by 2 changes the period by 1/2, what would we need to multiply by to get a period of 6 seconds? 6 seconds is 6/2(pi)=3/(pi) of 2(pi), to get 3/(pi) of the current period, we must multiply the interior argument by (pi)/3. This gives us a final model of:

d=2cos((pi/3)t)

If this model is correct, one period of the cosine wave will complete by t=6 seconds. This means that the model will return values of 2 at t=0 and t=6. Let's check:

d(0)=2cos((pi/3)(0))=2cos(0)=2*1=2

d(6)=2cos((pi/3)(6))=2cos(2(pi))=2*1=2

These values check out. This means that our model works. So, the final answer is:

d=2cos((pi/3)t)

User Avatar

Wiki User

14y ago
This answer is:
User Avatar

Add your answer:

Earn +20 pts
Q: Find a model for simple harmonic motion if the position at t equals 0 is 2 the amplitude is 2 centimeters and the period is 6 seconds?
Write your answer...
Submit
Still have questions?
magnify glass
imp
Related questions

The displcement x is m from the equilibrium position of a particle moving with SHM is given by x equals 0.05sint where t is the time in seconds measured from an instant when x equals o state the ampli?

The amplitude of the Simple Harmonic Motion is 0.05.


What is the position of the ball at 7.5 seconds?

What is the position of the ball at 7.5 seconds


What is the unit to measure speed of mouse?

centimeters/seconds


What is the position of the ball at 10 seconds?

10m


Can you run 100 millimeters in 10 seconds?

100 millimeters (1 meter/1000 millimeters)(100 centimeters/1 meter)(1 inch/2.54 centimeters) = 3.94 inches ---------------------Can you run 4 inches in 10 seconds?


How long will a metric ruler in centimeters take to measure a pen or pencil?

Less than 5 seconds. Less than 5 seconds. Less than 5 seconds. Less than 5 seconds.


What distance would a cockroach, crawling at a speed of 1.5 centimetres per second, cover in an hour?

To calculate the distance a cockroach, crawling at a speed of 1.5 centimeters per second, would cover in an hour, we need to convert the time from seconds to minutes and then to hours. There are 60 seconds in a minute, so the cockroach covers: 1.5 centimeters/second * 60 seconds/minute = 90 centimeters/minute. There are 60 minutes in an hour, so the cockroach covers: 90 centimeters/minute * 60 minutes/hour = 5400 centimeters/hour. Therefore, the cockroach would cover 5400 centimeters or 54 meters in an hour.


How many seconds should you Position yourself with a clear line-of-sight so you can search the traffic environment ahead?

You would need to position yourself 30 seconds ahead.


What is the relationship between the amplitude and frequency of a sine wave?

They are independent quantities. Amplitude decides the intensity ie energy content of the wave and frequency is different right from amplitude. If the maximum amplitude,E, is known then the instantaneous amplitude, e, can be found by e=E*sin(2*pi*f*t) where f is the frequency and t is the time in seconds from the start of the sine wave. Note that the angle in brackets is in radians. -------------------------------------------------------------------- Hi there is no such a term "maximum amplitude". Amplitude itself is the maximum displacement. For a fixed frequency and fixed amplitude, as time passes then the displacement e varies as fractiion of max E. That is all. E is constant and f is another constant. They are not directly related in any way.


How many centimeters are in a meter how many seconds are in an hour?

There are 100cm in a meter and 3600 seconds in an hour.


What is the duration of Assume the Position with Mr. Wuhl?

The duration of Assume the Position with Mr. Wuhl is 1800.0 seconds.


What is the equation for a sine wave operating at 375 Hz?

It is f(t) = a*sin(2*pi*375*t) where a is the amplitude and t is the time in seconds.