A mass suspended on a spring will exhibit sinusoidal motion when it moves. If the mass on a spring is 85cm off the ground at its highest position and 41cm off the ground at its lowest position and takes 3.0s to go from the top to the bottom and back again, determine an equation to model the data.
To model the data, we can use a sine function, as the motion of the mass on the spring exhibits sinusoidal motion.
Let's start by determining the amplitude of the motion. The amplitude is half the difference between the highest and lowest positions. In this case, the highest position is 85 cm and the lowest position is 41 cm. So, the amplitude is (85 - 41)/2 = 42 cm.
Next, we need to find the period of the motion. The period is the time it takes for the mass to complete one full cycle of motion. In this case, it takes 3.0 seconds to go from the top to the bottom and back again. So, the period is 3.0 seconds.
The general equation for the motion of a mass on a spring can be written as:
y(t) = A * sin(2πt/T)
where y(t) is the displacement of the mass at time t, A is the amplitude, t is the time, and T is the period.
Plugging in the values we found, the equation to model the given data becomes:
y(t) = 42 * sin(2πt/3.0)
amplitude=85-41 divided by 2=22
period=3sec
y=22sin(2pi*t/3)