First, record some data for this comparison in the table below. Record your measured values of displacement and velocity for times t = 8.0 seconds and t = 10.0 seconds in the columns below.
Next, use the measured displacement and velocity values at t = 7.0 seconds and t = 9.0 seconds to interpolate the values of displacement and velocity at t = 8.0 seconds.
Use the following formula to interpolate and extrapolate. Remember, x and y here represent values on the x and y axes of the graph. The x values will really be time and the y values will be either displacement (x) or velocity (vx).