Suggested languages for you:

Americas

Europe

10P

Expert-verifiedFound in: Page 436

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.**

- Time period is 0.75 sec.
- Frequency in Hz is 1.3 Hz.
- Angular frequency in rad/sec is 8.4 rad/s.

The time period of oscillation is 0.75 sec.

**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

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

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

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

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 $1.3\mathrm{Hz}$.

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

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

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

94% of StudySmarter users get better grades.

Sign up for free