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The displacement of an oscillating object as a function of time is shown in the figure.

a)What is the frequency?

b)What is the amplitude?

c)What is the period?

d)What is the angular frequency of this motion?

Concepts and ReasonThis problem was solved by the concept of characteristics of wave.

First, use the complete cycle’s time period to calculate frequency. To calculate the amplitude

A, you will need to find the highest wave height in a complete cycle. To calculate the value for angular frequency, you can use the expression of the angular frequency.FundamentalsThe frequency of a wave can be defined as the number waves that pass through a particular point at a given time. Here’s how to calculate frequency:

[katex]f = \frac{1}{T}[/katex]

Trefers to the time of a complete cycle.The amplitude of a Wave

Arefers to the highest height attained by a Wave in a Complete Cycle. It is measured in meters (m).Here is the expression of the angular frequency:

[katex]\omega = 2\pi f[/katex]

frefers to the frequency of a wave.(a) This is the time required to complete a cycle:

[katex]T = 16.0{\rm{ s}}[/katex]

Substitute 16.0s for T in equation [katex]f = \frac{1}{T}[/katex]

[katex]\begin{array}{c}\\f = \frac{1}{{16.0{\rm{ s}}}}\\\\ = 0.0625{\rm{ Hz}}\\\end{array}[/katex]

(b) The amplitude of the wave is the maximum height that a wave can reach in a complete cycle. Hence,

[katex]A = 10.0{\rm{ cm}}[/katex]

(c) The graph shows the following:

[katex]T = 16.0{\rm{ sec}}[/katex]

(d) Here is the expression of the angular frequency:

[katex]\omega = 2\pi f[/katex]

frefers to the frequency of a wave.Substitute 0.0625Hz for

fin this expression.[katex]\begin{array}{c}\\\omega = 2\pi \left( {0.0625{\rm{ Hz}}} \right)\\\\ = 0.39{\rm{ rad/s}}\\\end{array}[/katex]

Answer:Part a, Wave frequency is 0.0625 Hz.

Part b, Waves have an amplitude of 10.0 cm

Part c, The wave takes 16.0 seconds to complete a cycle.

Part d, Waves have an angular frequency at 0.39 rad/s.