/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 148 A particle moves on the \(x\)-ax... [FREE SOLUTION] | 91影视

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Chapter 9: Problem 148

A particle moves on the \(x\)-axis as per the equation \(x=x_{0} \sin ^{2} \omega t .\) The motion is simple harmonic (A) With amplitude \(x_{0}\) (B) With amplitude \(2 x_{0}\) (C) With time period \(\frac{2 \pi}{\omega}\) (D) With time period \(\frac{\pi}{\omega}\)

Short Answer

Expert verified
The motion of the particle is not simple harmonic, as the given equation \(x = x_0 \sin^2(\omega t)\) does not match the standard simple harmonic motion equations. Therefore, none of the given answer choices (A, B, C, or D) apply to the particle's motion.

Step by step solution

01

Analyze the given equation

The particle moves along the x-axis according to the given equation: \[x = x_0 \sin^2 (\omega t) \] This equation describes the motion of the particle in time.
02

Determine if the motion is simple harmonic

Simple harmonic motion can be described by the equation: \[x(t) = A \cos(\omega t + \phi)\] or \[x(t) = A \sin(\omega t + \phi)\] Where A is the amplitude, 蠅 is the angular frequency, t is time, 蠁 is the phase angle, and x(t) is the position of the particle at time t. However, the given equation is of the form: \[x = x_0 \sin^2 (\omega t)\] This equation does not match either of the simple harmonic motion equations. Therefore, the motion of the particle is not simple harmonic.
03

Answer relevant parts of the problem

Because the motion is not simple harmonic, answer choices A and B are not applicable. Amplitude or time period are not meaningful in this case, so choices C and D are also not applicable. In conclusion, none of the given answer choices apply to the particle's motion as described by the given equation.

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