The equation describing the motion of an object is y=0.8cos(4.2t+0.32). What is its period?
To find the period of the motion described by the equation, we need to analyze the equation and identify the components that determine the period.
The equation y = 0.8cos(4.2t + 0.32) represents a cosine function with a time variable t. The period of a cosine function is determined by the coefficient of the time variable inside the cosine function. In this case, the coefficient of t is 4.2.
The period of a cosine function is given by the formula:
Period = 2π / abs(coefficient of t)
In our equation, the coefficient of t is 4.2. We take the absolute value because the period is always positive.
Using the formula, we can calculate the period:
Period = 2π / abs(4.2)
= 2π / 4.2
= π / 2.1
Therefore, the period of the motion described by the equation y = 0.8cos(4.2t + 0.32) is π / 2.1 seconds.