Question

The displacement of a particle executing SHM is given by $x = 0.01 \sin(100\pi t + 0.05)$. Its maximum velocity is:

• A. $\pi$ m/s
• B. $10\pi$ m/s
• C. $0.1\pi$ m/s
• D. $100\pi$ m/s

Hint:

Max velocity occurs at the mean position where $x=0$.

Answer 1

The Correct Option is A

Step 1: Concept
The standard equation for SHM is $x = A \sin(\omega t + \phi)$, and the maximum velocity is $v_{max} = A\omega$.

Step 2: Meaning
From the given equation $x = 0.01 \sin(100\pi t + 0.05)$, we identify:
Amplitude $A = 0.01$ m
Angular frequency $\omega = 100\pi$ rad/s.

Step 3: Analysis
Calculate $v_{max}$:
$v_{max} = A \times \omega$
$v_{max} = 0.01 \times 100\pi$
$v_{max} = \pi$ m/s.

Step 4: Conclusion
The maximum velocity of the particle is exactly $\pi$ m/s. Final Answer: (A)