In an engine, a piston oscillates with simple harmonic motion so that its position varies according to the expression
x = 4.7 cos ( 4t + π/6 )
where x is in centimeters and t is in seconds. Find the period of the motion.
when 4 t = 2 pi we have gone around the circle from t = 0
so
4 T = 2 pi
T = 2 pi / 4 = pi/2
To find the period of the motion, we need to identify the coefficient in front of the variable 't' inside the cosine function.
In the given expression, x = 4.7 cos(4t + π/6), the coefficient in front of 't' is 4.
The formula to calculate the period of simple harmonic motion is given by:
T = (2π) / ω,
where T is the period and ω is the angular frequency.
The angular frequency is determined by the coefficient in front of 't' in the function. In this case, it is 4.
Now, we can calculate the period:
T = (2π) / 4,
T = π / 2.
Hence, the period of the simple harmonic motion is π/2 seconds.