Question:
Which one of the following motions is not simple harmonic motion?
Which one of the following motions is not simple harmonic motion?
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Logic Tip: All Simple Harmonic Motions are periodic, but not all periodic motions are Simple Harmonic. Uniform circular motion and rotation are the most common examples of periodic, non-oscillatory (and thus non-SHM) motions.
Updated On: Apr 27, 2026
- Rotation of earth about its axis
- Small oscillations of a mass attached to a spring
- Oscillation of mercury column in a U tube
- Oscillation of a second's pendulum
- The projection of uniform circular motion on the diameter of the circle
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The Correct Option is A
Solution and Explanation
Concept:
Simple Harmonic Motion (SHM) is a specific type of periodic motion where the restoring force is directly proportional to the displacement from an equilibrium (mean) position and is always directed towards that mean position ($F \propto -x$).
Step 1: Evaluate the characteristics of SHM.
To be SHM, a motion must: 1. Be periodic (repeat at regular intervals). 2. Be oscillatory (move back and forth about a mean position). 3. Have a restoring force/torque proportional to displacement.
Step 2: Analyze the given options.
Option (B): Mass on a spring has a restoring force $F = -kx$. This is the classic definition of SHM. Option (C): Liquid in a U-tube experiences a restoring force due to the weight difference of the liquid columns, proportional to the displacement. This is SHM. Option (D): A simple pendulum (like a second's pendulum) undergoes SHM for small angular displacements ($\sin\theta \approx \theta$). Option (E): The mathematical projection of uniform circular motion onto any diameter is exactly described by $x = A\cos(\omega t)$, which is the standard equation for SHM.
Step 3: Analyze the rotation of the Earth.
The rotation of the Earth about its axis is a \textit{periodic} motion because it repeats every 24 hours. However, it is not an \textit{oscillatory} motion. It continuously moves in one direction (it does not swing back and forth across a central mean position). Therefore, there is no restoring force involved.
Simple Harmonic Motion (SHM) is a specific type of periodic motion where the restoring force is directly proportional to the displacement from an equilibrium (mean) position and is always directed towards that mean position ($F \propto -x$).
Step 1: Evaluate the characteristics of SHM.
To be SHM, a motion must: 1. Be periodic (repeat at regular intervals). 2. Be oscillatory (move back and forth about a mean position). 3. Have a restoring force/torque proportional to displacement.
Step 2: Analyze the given options.
Option (B): Mass on a spring has a restoring force $F = -kx$. This is the classic definition of SHM. Option (C): Liquid in a U-tube experiences a restoring force due to the weight difference of the liquid columns, proportional to the displacement. This is SHM. Option (D): A simple pendulum (like a second's pendulum) undergoes SHM for small angular displacements ($\sin\theta \approx \theta$). Option (E): The mathematical projection of uniform circular motion onto any diameter is exactly described by $x = A\cos(\omega t)$, which is the standard equation for SHM.
Step 3: Analyze the rotation of the Earth.
The rotation of the Earth about its axis is a \textit{periodic} motion because it repeats every 24 hours. However, it is not an \textit{oscillatory} motion. It continuously moves in one direction (it does not swing back and forth across a central mean position). Therefore, there is no restoring force involved.
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