Question

The frequency of SHM is $100\;{\text{Hz}}$ then the time period is
A) $0.01\;{\text{s}}$
B) $0.1\;{\text{s}}$
C) $1\;{\text{s}}$
D) $100\;{\text{s}}$

Answer 1

Hint:The number of cycles completed per unit time is called frequency. The time taken to complete one oscillation is called time period. Time period is inversely proportional to the frequency. By substituting the inverse value of frequency, we can get the value of the time period.

Useful formula:
The expression for finding time period is
 ${T_p} = \dfrac{1}{f}$
Where ${T_p}$is the time period and $f$ is the frequency of SHM

Complete step by step answer:
Given, The frequency of SHM is $f = 100\;{\text{Hz}}$
The ratio of the number of cycles completed to the time taken is called frequency.
     $Frequency = \dfrac{n}{t}$
where $n$ is the number of cycles completed and $t$is the time taken.

The inverse value of frequency is called time period.
The expression for finding time period is

${T_p} = \dfrac{1}{f}$
Substitute all the values in the above equation.
$
  {T_p} = \dfrac{1}{{100\;{\text{Hz}}}} \\
  {T_p} = 0.01\;{\text{s}} \\
$
Thus, the time period is ${T_p} = 0.01\;{\text{s}}$.

Thus, the option A is correct.

Additional information:
Resonance can be defined as the tendency of vibration of the system when a frequency of excitation is achieved. The amplitude increases in the case of resonance. In resonance, the increasing frequency of an object tries to match the frequency of another vibration.


Note:
The speed at which resonance occurs is known as critical speed or whirling speed. Resonance has various applications in day to day life. For example, when, turbine attains its maximum speed, it has to cross the whirling speed, and it is known that at whirling speed, the amplitude of vibration reaches a maximum value. So the turbine could burst at this speed. So to protect it, the speed of the turbine is increased by a huge amount when the speed of the turbine comes near to whirling speed.