Amplitude and Cosine Functions

The video tutorial explains a problem involving simple harmonic motion, where the position of a weight attached to a spring is described by a cosine function. The tutorial covers finding the maximum height above equilibrium, calculating the period and frequency, and determining the time when the weight reaches its maximum height. The instructor also discusses the importance of units in these calculations.

What is the function given for the position of a weight attached to a spring in simple harmonic motion?

• s(t) = 4 sin(10t)

• s(t) = 4 cos(10t)

• s(t) = -4 sin(10t)

• s(t) = -4 cos(10t)

What is the role of the variable t in the function s(t) = -4 cos(10t)?

• It represents the amplitude

• It represents the phase shift

• It represents the frequency

• It represents time in seconds

What does the amplitude of a wave function represent in simple harmonic motion?

• The period of the wave

• The speed of the wave

• The maximum height above equilibrium

• The frequency of oscillation

How is the amplitude of the function s(t) = -4 cos(10t) calculated?

• By taking the square root of 4

• By dividing 4 by 10

• By taking the absolute value of -4

• By multiplying 4 by 10

What is the maximum value that the function s(t) = -4 cos(10t) can reach?

• 10

• -4

• 0

• 4

What is the significance of the number 4 in the function s(t) = -4 cos(10t)?

• It represents the phase shift

• It represents the frequency

• It represents the amplitude

• It represents the period

What does the negative sign in the function s(t) = -4 cos(10t) indicate?

• A phase shift

• A decrease in frequency

• A reflection over the x-axis

• An increase in amplitude

What is the formula used to calculate the period of a cosine function in simple harmonic motion?

• ω/π

• π/ω

• ω/2π

• 2π/ω

If ω = 10 in the function s(t) = -4 cos(10t), what is the period?

• 5π

• π/5

• 2π/10

• π/10

What is the general form of a cosine function used to describe simple harmonic motion?

• A cot(ωt)

• A tan(ωt)

• A cos(ωt)

• A sin(ωt)