Question:
A particle executes SHM with amplitude \( 0.1 \text{ m} \) and angular frequency \( 10 \text{ rad/s} \). Maximum acceleration is:
A particle executes SHM with amplitude \( 0.1 \text{ m} \) and angular frequency \( 10 \text{ rad/s} \). Maximum acceleration is:
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Keep your position boundaries clear in SHM! The velocity is maximum at the mean position (\(x=0\)) where acceleration is zero. Conversely, acceleration reaches its peak magnitude (\(\omega^2 A\)) at the extreme endpoints (\(x = \pm A\)) where the velocity drops to zero!
Updated On: May 20, 2026
- \( 1 \text{ m/s}^2 \)
- \( 5 \text{ m/s}^2 \)
- \( 10 \text{ m/s}^2 \)
- \( 100 \text{ m/s}^2 \)
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The Correct Option is C
Solution and Explanation
Concept:
In Simple Harmonic Motion (SHM), the acceleration \( a \) of a particle at any instant is directly proportional to its displacement \( x \) from the mean position and acts in the opposite direction. The governing kinematic equation is:
\[
a = -\omega^2 x
\]
where \(\omega\) represents the angular frequency of the system.
To find the magnitude of the maximum acceleration (\( a_{\max} \)), we consider the point where the displacement is at its absolute maximum value. This maximum displacement is defined as the amplitude \( A \) of the oscillation:
\[
a_{\max} = \omega^2 A
\]
Step 1: Extracting the given kinematic parameters from the problem text.
From the question statement, we have:
• Amplitude of oscillation, \( A = 0.1 \text{ m} \)
• Angular frequency, \( \omega = 10 \text{ rad/s} \)
Step 2: Substituting the parameters into the maximum acceleration formula.
Apply the values directly to the equation: \[ a_{\max} = (10)^2 \cdot (0.1) \] Evaluating the square of the angular frequency: \[ (10)^2 = 100 \] Now, performing the multiplication: \[ a_{\max} = 100 \cdot 0.1 = 10 \text{ m/s}^2 \] Wait, let's re-read the options and calculation carefully: \( 100 \times 0.1 = 10 \). This corresponds to option (C). Let me correct the answer label in the final block.
Step 3: Final validation of the correct option choice.
Our calculation gives: \[ a_{\max} = 10 \text{ m/s}^2 \] This perfectly matches option (C).
Step 1: Extracting the given kinematic parameters from the problem text.
From the question statement, we have:
• Amplitude of oscillation, \( A = 0.1 \text{ m} \)
• Angular frequency, \( \omega = 10 \text{ rad/s} \)
Step 2: Substituting the parameters into the maximum acceleration formula.
Apply the values directly to the equation: \[ a_{\max} = (10)^2 \cdot (0.1) \] Evaluating the square of the angular frequency: \[ (10)^2 = 100 \] Now, performing the multiplication: \[ a_{\max} = 100 \cdot 0.1 = 10 \text{ m/s}^2 \] Wait, let's re-read the options and calculation carefully: \( 100 \times 0.1 = 10 \). This corresponds to option (C). Let me correct the answer label in the final block.
Step 3: Final validation of the correct option choice.
Our calculation gives: \[ a_{\max} = 10 \text{ m/s}^2 \] This perfectly matches option (C).
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