Question

An oscillating block–spring system takes 0.75 sto begin repeating its motion.

1. Find the period.
2. Find the frequency in hertz.
3. Find the angular frequency in radians per second.

Short answer

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

Step-by-step solution

Stating the given data

The time period of oscillation is 0.75 sec.

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

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

a) Calculation of time period

Time taken to complete one cycle isthetime period that is the time taken for repeatingthemotion.

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

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 $1.3\mathrm{Hz}$.

c) Calculation of angular frequency

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

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

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