Demonstrating Position, Velocity, and Acceleration of a Mass-Spring System

The video tutorial demonstrates a vertical mass spring system in simple harmonic motion. The instructor explains the setup, reviews key equations, and collects data on position, velocity, and acceleration. Graphs are analyzed to understand the motion, and the period of the system is determined. The spring constant is calculated using the period, and a best fit sine wave is added to the data for further analysis. The tutorial highlights the damping effect observed in the system and provides insights into the errors in velocity and acceleration measurements.

What is the purpose of adding a playing card below the mass in the vertical mass spring system?

• To stabilize the spring

• To make the system more visually appealing

• To increase the mass of the system

• To help the motion sensor detect the position more easily

Which equation represents the position as a function of time in simple harmonic motion?

• Position = Amplitude * tan(angular frequency * time + phase constant)

• Position = Amplitude * cos(angular frequency * time + phase constant)

• Position = Amplitude * exp(angular frequency * time + phase constant)

• Position = Amplitude * sin(angular frequency * time + phase constant)

Why does the acceleration graph show more error compared to the position graph?

• Because acceleration is calculated from velocity, which is derived from position

• Because the motion sensor directly measures acceleration

• Because acceleration is a more complex quantity

• Because the spring constant affects acceleration more

How is the period of the mass spring system determined from the data?

• By using the spring constant directly

• By measuring the time for half a cycle and doubling it

• By measuring the time for two complete cycles and dividing by two

• By measuring the time for one complete cycle

What is the calculated spring constant of the spring in the system?

• 6.51 newtons per meter

• 5.51 newtons per meter

• 8.51 newtons per meter

• 7.51 newtons per meter

What does the constant 'C' in the best-fit sine wave equation represent?

• The frequency of the wave

• The vertical shift of the wave

• The phase shift of the wave

• The amplitude of the wave

What is the significance of the damping observed in the mass spring system?

• It means the motion sensor is malfunctioning

• It shows the system loses energy over time

• It indicates the system is in perfect harmonic motion

• It suggests the spring constant is too high