Which of the following statements is correct? (a) Every...

Name: Problem 99, Chapter 14: Objective NCERT at your FINGERTIPS: Physics
Uploaded: 2021-09-28T10:53:48-08:00
Duration: 1 min 59 s
Channel: Mahendra Kumar
Description: Which of the following statements is correct? (a) Every periodic motion is simple harmonic motion. (b) In simple harmonic motion the period is proportional to the square of the amplitude of oscillation. (c) In simple harmonic motion the phase constant depends on initial condition. (d) The resonance frequency of a driven oscillator depends on the damping.

Which of the following statements is correct? (a) Every periodic motion is simple harmonic motion. (b) In simple harmonic motion the period is proportional to the square of the amplitude of oscillation. (c) In simple harmonic motion the phase constant depends on initial condition. (d) The resonance frequency of a driven oscillator depends on the damping.

Which of the following statements is correct?
(a) Every periodic motion is simple harmonic motion.
(b) In simple harmonic motion the period is proportional to the square of the amplitude of oscillation.
(c) In simple harmonic motion the phase constant depends on initial condition.
(d) The resonance frequency of a driven oscillator depends on the damping.

Key Concepts

Damping

Damping refers to any effect, such as friction or resistance, that reduces the amplitude of oscillations over time. In the context of driven oscillators, damping influences the sharpness and position of the resonance peak, often causing the resonance frequency to shift from the undamped natural frequency.

Periodic Motion

Periodic motion refers to any motion that repeats itself at regular intervals. It is a broad category that encompasses various types of oscillatory motions, including but not limited to simple harmonic motion. The defining feature is that the system returns to its initial state after a fixed period, irrespective of the specific functional form of the motion.

Simple Harmonic Motion

Simple harmonic motion (SHM) is a specific type of periodic motion where the restoring force is directly proportional to the displacement from the equilibrium position and acts in the opposite direction. This results in sinusoidal motion with key characteristics such as constant frequency and amplitude, provided no damping is present.

Amplitude

Amplitude is the maximum displacement of the system from its equilibrium position. In ideal simple harmonic motion, the period and frequency of the motion are independent of the amplitude, meaning that changes in amplitude do not affect the period of oscillation.

Phase Constant

The phase constant in simple harmonic motion represents the initial phase of the oscillation, which accounts for where in its cycle the motion begins. This parameter is determined by the initial conditions of the system, such as the initial displacement and velocity.

Resonance Frequency

Resonance frequency is the frequency at which a system naturally oscillates with the greatest amplitude when driven by an external force. In a driven oscillator, this frequency can depend on factors such as the system’s inherent properties and any damping present in the system.

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