Understanding Displacement, Amplitude, Period, and Frequency

The video tutorial explains the displacement of a mass by a spring using a sinusoidal function. It covers the concepts of amplitude, period, and frequency, and how they relate to the motion of the mass. The tutorial includes a review of key vocabulary, graphical representation of displacement, and calculations for amplitude, period, and frequency. The video concludes with a summary of the key points discussed.

What is the function that models the displacement of a mass by a spring?

• h(T) = 8 cos(6πT)

• h(T) = 6 sin(8πT)

• h(T) = 6 cos(8πT)

• h(T) = 8 sin(6πT)

In the context of the mass-spring system, what does displacement refer to?

• The total distance traveled by the mass

• The speed of the mass

• The directed distance from the equilibrium position

• The weight of the mass

What is the period of a function in the context of a mass-spring system?

• The time it takes for the mass to reach its maximum displacement

• The time it takes for the mass to reach its minimum displacement

• The time it takes for one complete cycle of motion

• The time it takes for the mass to stop moving

How is frequency defined in the context of the mass-spring system?

• The number of cycles per minute

• The number of cycles per second

• The number of cycles per hour

• The number of cycles per day

What does the positive part of the displacement graph indicate?

• The mass is below the equilibrium position

• The mass is at the equilibrium position

• The mass is not moving

• The mass is above the equilibrium position

What is the amplitude of the function h(T) = 8 sin(6πT)?

• 12 cm

• 8 cm

• 16 cm

• 6 cm

How is the period of the function h(T) = 8 sin(6πT) calculated?

• 8 / 6π

• 6π / 2π

• 6π / 8

• 2π / 6π

What is the period of the function h(T) = 8 sin(6πT)?

• 1/3 second

• 1/2 second

• 1/5 second

• 1/4 second

What is the frequency of the function h(T) = 8 sin(6πT)?

• 2 Hz

• 4 Hz

• 5 Hz

• 3 Hz

How many complete cycles does the mass complete in one second?

• One cycle

• Two cycles

• Three cycles

• Four cycles