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: Understanding the Concept:
In Simple Harmonic Motion (SHM), displacement follows a sine or cosine wave. Velocity is the rate of change of displacement, and its maximum value occurs at the equilibrium position.
Step 2: Key Formula or Approach:
Standard equation: \(x = A \sin(\omega t + \phi)\).
Maximum velocity formula: \(v_{max} = A \omega\).
Step 3: Detailed Explanation:
Given: \(x = 0.01 \sin(100\pi t + 0.05)\).
Comparing this with the standard form:
Amplitude (\(A\)) = 0.01 m
Angular frequency (\(\omega\)) = \(100\pi \text{ rad/s}\)

Now, calculate maximum velocity:
\[ v_{max} = A \times \omega \]
\[ v_{max} = 0.01 \times 100\pi \]
\[ v_{max} = 1\pi = \pi\text{ m/s} \]
Step 4: Final Answer:
The maximum velocity is \(\pi\text{ m/s}\).