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)
100 millimeters is 10 centimeters or about four inches. So you can run 100mm in under 10 seconds.
The snail moves 0.3m per minute.
There are 60 seconds in a minuteso (3 minutes = 180 seconds) + 15 seconds= 195 seconds
There are 86,400 seconds in one day; simply multiply that by the number of days and you have your answer. 4daysX24hours/day=96hours 96hoursx3600(seconds/hour)=345,600 seconds
31,536,000 seconds
The amplitude of the Simple Harmonic Motion is 0.05.
What is the position of the ball at 7.5 seconds
centimeters/seconds
10m
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?
Less than 5 seconds. Less than 5 seconds. Less than 5 seconds. Less than 5 seconds.
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.
You would need to position yourself 30 seconds ahead.
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.
There are 100cm in a meter and 3600 seconds in an hour.
The duration of Assume the Position with Mr. Wuhl is 1800.0 seconds.
It is f(t) = a*sin(2*pi*375*t) where a is the amplitude and t is the time in seconds.