Assertion The amplitude of a particle executing SHM with a...

Assertion The amplitude of a particle executing SHM with a frequency of $60 \mathrm{~Hz}$ is $0.01 \mathrm{~m}$. The maximum value of acceleration of the particle is $\pm 144 \pi^{2} \mathrm{~ms}^{-2}$. Reason Acceleration amplitude $=\omega^{2} A$,where $A$ is displacement amplitude.

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Key Concepts

Angular Frequency

Angular frequency (?) is a key parameter in SHM that connects the regular frequency of oscillation to the phase of the motion through the relation ? = 2?f, where f is the frequency in hertz. It quantifies how quickly the oscillator cycles through its periodic motion in radians per second and directly impacts the expressions for both velocity and acceleration in the motion.

Acceleration in SHM

In the context of SHM, the acceleration of the oscillating particle is calculated using the formula a = -?²x, where x is the displacement. This relationship indicates that the maximum acceleration is obtained when the displacement equals the amplitude, leading to the magnitude of the maximum acceleration being ?² times the displacement amplitude. This concept is crucial for analyzing the dynamics of oscillating systems.

Simple Harmonic Motion

Simple Harmonic Motion (SHM) refers to the type of periodic oscillation where the restoring force is directly proportional to the displacement from the equilibrium position and acts in the opposite direction. This results in sinusoidal oscillations for displacement, velocity, and acceleration, making it a fundamental concept in the study of oscillatory systems in physics.

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