Question

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?

Answer 1

Concepts and reason

The concept used to solve this problem is characteristics of wave.

First, calculate the frequency using the time period for a complete cycle. In the next part, find the maximum height attained by wave in a complete cycle to calculate amplitude A. In the last part, use the expression of angular frequency to calculate the value of angular frequency.

Fundamentals

The frequency of a wave is defined as the number of waves passing through a point in a certain time. The expression to calculate frequency is given as follows:

$f = \frac{1}{T}$

Here, T is the time of one complete cycle.

The amplitude of a wave A is defined as the maximum height attained by a wave in complete cycle. It is measured in meters(m).

The expression of the angular frequency is given as follows:

$\omega = 2\pi f$

Here, f is the frequency of wave.

(a)

The time for a complete cycle is given as:

$T = 16.0{\rm{ s}}$

Substitute 16.0 s for T in the equation $f = \frac{1}{T}$ .

$\begin{array}{c}\\f = \frac{1}{{16.0{\rm{ s}}}}\\\\ = 0.0625{\rm{ Hz}}\\\end{array}$

(b)

The maximum height attained by the wave in complete cycle is equal to the amplitude of wave. Hence,

$A = 10.0{\rm{ cm}}$

(c)

From the graph, the period of wave is given as:

$T = 16.0{\rm{ sec}}$

(d)

The expression of the angular frequency is given as follows:

$\omega = 2\pi f$

Here, f is the frequency of wave.

Substitute 0.0625 Hz for f in the above expression.

$\begin{array}{c}\\\omega = 2\pi \left( {0.0625{\rm{ Hz}}} \right)\\\\ = 0.39{\rm{ rad/s}}\\\end{array}$

Ans: Part a

The frequency of wave is 0.0625 Hz.

Part b

The amplitude of wave is 10.0 cm.

Part c

The period of the wave to complete one cycle is 16.0 s.

Part d

The angular frequency of wave is 0.39 rad/s.