Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 10: Problem 1337

If the equation for a particle performing S.H.M. is given by $\mathrm{y}=\sin 2 \mathrm{t}+\sqrt{3} \cos 2 \mathrm{t}\(, its periodic time will be \)\ldots \ldots .$ s. (A) 21 (B) \(\pi\) (C) \(2 \pi\) (D) \(4 \pi\).

Short Answer

Expert verified
The periodic time of the given S.H.M. is \(2\pi\) seconds. The correct answer is (C) \(2\pi\).

Step by step solution

01

Determine the period of each term

In the given equation, y(t) = sin(2t) + √3 * cos(2t). The two individual trigonometric functions are sin(2t) and cos(2t). Both of these functions have a period of \(2\pi\), because any multiple of their argument will give the same value and they only repeat at those values. For example: sin(x) = sin(x+2π) cos(x) = cos(x+2π)
02

Determine the period of their sum

To find the period of the sum, we're looking for the smallest positive value of t for which both sin(2t) and cos(2t) repeat. Since both functions have a period of \(2\pi\), their sum will also have the same period. So, the period of the given equation y(t) = sin(2t) + √3 * cos(2t) is \(2\pi\).
03

Convert the period to periodic time

The periodic time is the time taken to complete one oscillation or cycle. It is represented by the variable T. As per the given equation, when the period of the S.H.M. is \(2\pi\), the periodic time T is also \(2\pi\). So the periodic time of the given S.H.M. is \(2\pi\) seconds. The correct answer is (C) \(2\pi\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Length of a steel wire is \(11 \mathrm{~m}\) and its mass is \(2.2 \mathrm{~kg}\). What should be the tension in the wire so that the speed of a transverse wave in it is equal to the speed of sound in dry air at \(20^{\circ} \mathrm{C}\) temperature? (A) \(2.31 \times 10^{4} \mathrm{~N}\) (B) \(2.25 \times 10^{4} \mathrm{~N}\) (C) \(2.06 \times 10^{4} \mathrm{~N}\) (D) \(2.56 \times 10^{4} \mathrm{~N}\)

A small spherical steel ball is placed at a distance slightly away from the center of a concave mirror having radius of curvature \(250 \mathrm{~cm}\). If the ball is released, it will now move on the curved surface. What will be the periodic time of this motion? Ignore frictional force and take $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}$. (A) \((\pi / 4) \mathrm{s}\) (B) \(\pi \mathrm{s}\) (C) \((\pi / 2) \mathrm{s}\) (D) \(2 \pi \mathrm{s}\)

For a particle executing \(\mathrm{S} . \mathrm{H} \mathrm{M} .\), when the potential energy of the oscillator becomes \(1 / 8\) the maximum potential energy, the displacement of the oscillator in terms of amplitude A will be........... (A) \((\mathrm{A} / \sqrt{2})\) (B) \(\\{\mathrm{A} /(2 \sqrt{2})\\}\) (C) \((\mathrm{A} / 2)\) (D) \(\\{\mathrm{A} /(3 \sqrt{2})\\}\)

Which of the following functions represents a travelling wave? (A) \((\mathrm{x}-\mathrm{vt})^{2}\) (B) in \((\mathrm{x}+\mathrm{vt})\) (C) \(\mathrm{e}^{-(\mathrm{x}+\mathrm{vt}) 2}\) (D) \(\\{1 /(\mathrm{x}+\mathrm{vt})\\}\)

A system is executing S.H.M. with a periodic time of \(4 / 5 \mathrm{~s}\) under the influence of force \(\mathrm{F}_{1}\) When a force \(\mathrm{F}_{2}\) is applied, the periodic time is \((2 / 5) \mathrm{s}\). Now if \(\mathrm{F}_{1}\) and \(\mathrm{F}_{2}\) are applied simultaneously along the same direction, the periodic time will be......... (A) \(\\{4 /(5 \sqrt{5})\\}\) (B) \(\\{4 /(4 \sqrt{5})\\}\) (C) \(\\{8 /(4 \sqrt{5})\\}\) (D) \(\\{8 /(5 \sqrt{5})\\}\)
See all solutions

Recommended explanations on English Textbooks

Free Response Essay

Read Explanation

Email

Read Explanation

Essay Writing Skills

Read Explanation

Language and Social Groups

Read Explanation

Argumentative Essay

Read Explanation

Synthesis Essay

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free