The diagram below shows a mass, a spring, and a near-frictionless surface. If you pull the mass back 10 cm and then release it, the mass starts to oscillate. The distance of the mass from the wall is modeled by the equation y = 3sin(4pi t + pi/2) + 7 cm, where t is the time in seconds.
Where is the mass when t = 2 seconds?
Is there any reason you cant paste this into the Google search window?
3*sin((8PI)+PI)+7
To find the location of the mass when t = 2 seconds, we need to substitute t = 2 into the given equation.
The equation given is y = 3sin(4πt + π/2) + 7.
Substituting t = 2 into the equation, we have:
y = 3sin(4π(2) + π/2) + 7.
Simplifying the expression inside the parentheses:
y = 3sin(8π + π/2) + 7.
Now, let's simplify further:
y = 3sin(8π)cos(π/2) + 3cos(8π)sin(π/2) + 7.
Since sin(8π) = 0 and cos(8π) = 1, we can simplify this equation to:
y = 3(0)(1) + 3(1)(1) + 7.
Next, simplify the equation:
y = 0 + 3 + 7.
With further simplification, we get:
y = 10.
Therefore, when t = 2 seconds, the mass is located at y = 10 cm.