Rankers Physics

Equation of SHM: Practice Problem & Solution

Which one of the following equations of motion represents simple harmonic motion? where $k$, $k_0$, $k_1$ and $a$ are all positive. (2009)
Acceleration $= -k(x)$
Acceleration $= k(x + a)$
Acceleration $= kx$
Acceleration $= -k_0x + k_1x^2$

Solution Explained:

To solve this problem, we apply the core principles of Equation of SHM. Understanding the underlying formula is key to arriving at the correct answer below:

For simple harmonic motion, the acceleration must be directly proportional and opposite in direction to the displacement. Thus, $a \propto -x$, which matches the equation $\text{Acceleration} = -k(x)$.

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Similar Practice Questions

Explore conceptually related problems to test your knowledge.

1. A pendulum is hung from the roof of a sufficiently high building and is moving freely to and fro like a simple harmonic oscillator. The acceleration of the bob of the pendulum is $20 \text{ m/s}^2$ at a distance of $5 \text{ m}$ from the mean position. The time period of oscillation is: (2018)
2. If the length of a simple pendulum is increased by 2%, then the time period: (1997)
3. Assertion (A): If the amplitude of a simple harmonic oscillator is doubled, its total energy also becomes doubled. Reason (R): In harmonic oscillation, the total energy is directly proportional to the amplitude of vibration.  
4. Assertion (A): A SHM may be assumed as composition of many SHM's. Reason (R): Superposition of many SHM's (along same line) of same frequency will be a SHM.  
5. Assertion (A): For a particle performing SHM, its speed decreases as it goes away from the mean position. Reason (R): In SHM, the acceleration is always opposite to the velocity of the particle.