Question

The phase of a particle performing a linear S.H.M increases by \(\frac{\pi ^{c}}{6}\) after every 5 second. The frequency of its oscillation is

• A. \(1\text{Hz}\)
• B. \(\frac{1}{20}\text{Hz}\)
• C. \(\frac{1}{30}\text{Hz}\)
• D. \(\frac{1}{60}\text{Hz}\)

Hint:

Phase increases uniformly at the rate omega, so find omega first and then divide by 2 pi.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept
The phase of SHM is \(\omega t+\phi\), so a phase change \(\Delta\phi\) in time \(\Delta t\) gives \(\omega=\dfrac{\Delta\phi}{\Delta t}\).

Step 2: Find omega
\(\omega=\dfrac{\pi/6}{5}=\dfrac{\pi}{30}\text{ rad/s}\)

Step 3: Find frequency
\(f=\dfrac{\omega}{2\pi}=\dfrac{1}{60}\text{ Hz}\)

Final Answer:
The frequency is \(\dfrac{1}{60}\text{ Hz}\). \[ \boxed{\text{(D) }\dfrac{1}{60}\text{Hz}} \]