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Found in: Page 436

### Fundamentals Of Physics

Book edition 10th Edition
Author(s) David Halliday
Pages 1328 pages
ISBN 9781118230718

# An oscillating block–spring system takes 0.75 s to begin repeating its motion. Find the period.Find the frequency in hertz.Find the angular frequency in radians per second.

1. Time period is 0.75 sec.
2. Frequency in Hz is 1.3 Hz.
See the step by step solution

## Step 1: Stating the given data

The time period of oscillation is 0.75 sec.

## Step 2: Understanding the concept of simple harmonic motion

The time period is the time required to complete one complete cycle. We use this concept to find the time period. Once we know the time period, we can find the frequency and angular frequency by using the basic formula in SHM.

Formula:

The time period of a body in oscillation

$\mathrm{T}=\frac{1}{\mathrm{f}}$ (i)

Angular frequency of a body in oscillation

$\mathrm{\omega }=2×\mathrm{\pi }×\mathrm{f}$ (ii)

## Step 3: a) Calculation of time period

Time taken to complete one cycle is the time period that is the time taken for repeating the motion.

So, the time period is $\mathrm{T}=0.75\mathrm{sec}$.

## Step 4: b) Calculation of frequency

Using equation (i), the frequency of a body is given as

$\begin{array}{rcl}\mathrm{f}& =& \frac{1}{\mathrm{T}}\\ & =& \frac{1}{0.75}\\ & =& 1.3\mathrm{Hz}\end{array}$

Hence, the value of frequency is $1.3\mathrm{Hz}$.

## Step 5: c) Calculation of angular frequency

Using equation (ii), the angular frequency is given as

$\begin{array}{rcl}\mathrm{\omega }& =& 2\mathrm{\pi }×1.3\\ & =& 8.17\mathrm{rad}/\mathrm{sec}\end{array}$

Hence, the value of angular frequency is $8.17\mathrm{rad}/\mathrm{sec}$.