amplitude=85-41 divided by 2=22
period=3sec
y=22sin(2pi*t/3)
period=3sec
y=22sin(2pi*t/3)
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(2Ï€t/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(2Ï€t/3.0)