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Modeling Periodic Motion and Height Variation in Trigonometric Functions Quiz

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Which trigonometric function is used to model the height variation of an object in periodic motion?

Sine function

Explanation

Sine function models vertical displacement in periodic motion.

In a simple harmonic motion, if the amplitude of oscillation is 10 meters, what is the maximum displacement of the object from its equilibrium position?

10 meters

Explanation

Maximum displacement equals the amplitude of oscillation.

What is the period of a sinusoidal function that completes one cycle in 2π seconds?

4π

Explanation

Period is the time taken to complete one cycle.

Which trigonometric function represents the vertical displacement of an object in simple harmonic motion?

Sine function

Explanation

Sine function represents vertical displacement.

For a sinusoidal function f(x) = 3sin(2x - π/4), what is the amplitude?

Explanation

Amplitude is the coefficient of the sine function.

In a pendulum, if the length of the string is doubled, how does it affect the period of oscillation?

The period remains the same

Explanation

Period is independent of the length of the string.

What is the phase shift of the function f(x) = sin(2x - π/4)?

π/4

Explanation

Phase shift determines the horizontal translation of the function.

If the period of a periodic function is 2 seconds, what is its frequency in hertz?

2 Hz

Explanation

Frequency is the reciprocal of the period.

What is the phase shift of the function f(x) = cos(3x - π/6)?

π/6

Explanation

Phase shift is the horizontal translation of the function.

#10

If the angular frequency of a harmonic motion is 5 rad/s and the amplitude is 2 meters, what is the maximum velocity of the object?

10 m/s

Explanation

Maximum velocity equals the product of angular frequency and amplitude.

#11

What is the phase difference between the functions f(x) = 2sin(x) and g(x) = 2sin(x + π/3)?

π/3

Explanation

Phase difference is the horizontal shift between two functions.

#12

If a sinusoidal function completes 4 cycles in 6 seconds, what is its frequency?

3 Hz

Explanation

Frequency is the reciprocal of the time taken for multiple cycles.

Modeling Periodic Motion and Height Variation in Trigonometric Functions Quiz

Which trigonometric function is used to model the height variation of an object in periodic motion?

In a simple harmonic motion, if the amplitude of oscillation is 10 meters, what is the maximum displacement of the object from its equilibrium position?

What is the period of a sinusoidal function that completes one cycle in 2π seconds?

Which trigonometric function represents the vertical displacement of an object in simple harmonic motion?

For a sinusoidal function f(x) = 3sin(2x - π/4), what is the amplitude?

In a pendulum, if the length of the string is doubled, how does it affect the period of oscillation?

What is the phase shift of the function f(x) = sin(2x - π/4)?

If the period of a periodic function is 2 seconds, what is its frequency in hertz?

What is the phase shift of the function f(x) = cos(3x - π/6)?

If the angular frequency of a harmonic motion is 5 rad/s and the amplitude is 2 meters, what is the maximum velocity of the object?

What is the phase difference between the functions f(x) = 2sin(x) and g(x) = 2sin(x + π/3)?

If a sinusoidal function completes 4 cycles in 6 seconds, what is its frequency?

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