Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 15: Q4Q (page 435)

Which of the following relationships between the acceleration a and the displacement x of a particle involve SHM: (a) a=0.5x, (b) a=400x2, (c) a=20x, (d)a=-3x2?

Short Answer

Expert verified

The relationship between acceleration and displacement is a=-20x .

Step by step solution

01

The given data 

The relationships between acceleration and position are given as:

  1. a=0.5x
  2. a=400x2
  3. a=-20x
  4. a=-3x2
02

Understanding the concept of Hooke’s law

We can use Hook’s law to determine the relation between acceleration and displacement of the particle. Comparing it with the given options, we can find the correct option showing this relationship.

Formulae:

The force on a spring due to Hooke’s law F=-kx, (i)

The force due to Newton’s second law of motion, F=ma (ii)

03

Calculation of the correct acceleration and displacement relation

ma=-kxa=-kmx

Comparing this result with the options given in the problem,

The option (c) matches with the acceleration we wrote from Hook’s law.

Therefore, the relation a=-20x involves the SHM.

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

A loudspeaker diaphragm is oscillating in simple harmonic motion with a frequency of440Hzand a maximum displacement of0.75mm.

  1. What is the angular frequency?
  2. What is the maximum speed?
  3. What is the magnitude of the maximum acceleration?

A common device for entertaining a toddler is a jump seat that hangs from the horizontal portion of a doorframe via elastic cords (Fig. 15-63). Assume that only one cord is on each side in spite of the more realistic arrangement shown. When a child is placed in the seat, they both descend by a distance dsas the cords stretch (treat them as springs). Then the seat is pulled down an extra distance dmand released, so that the child oscillates vertically, like a block on the end of a spring. Suppose you are the safety engineer for the manufacturer of the seat. You do not want the magnitude of the child’s acceleration to exceed 0.20 gfor fear of hurting the child’s neck. If dm=10cm, what value of dscorresponds to that acceleration magnitude?

Figure 15-24shows the x(t) curves for three experiments involving a particular spring–box system oscillating in SHM. Rank the curves according to (a) the system’s angular frequency, (b) the spring’s potential energy at time t=0, (c) the box’s kinetic energy att=0, (d) the box’s speed att=0, and (e) the box’s maximum kinetic energy, greatest first.

In Fig. 15-64, ademolition ball swings from the end of a crane. The length of the swinging segment of cable is 17. (a) Find the period of the swinging, assuming that the system can be treated as a simple pendulum. (b) Does the period depend on the ball’s mass?

Question: The angle of the pendulum in Figure is given by θ=θmcos[(4.44rad/s)t+Φ]. If at t = 0θ=0.040rad , anddθ/dt=0.200rad/s ,

  1. what is the phase constant φ,
  2. what is the maximum angleθm ?

(Hint: Don’t confuse the rate dθat which changes with the θof the SHM.)
See all solutions

Recommended explanations on Physics Textbooks

Magnetism and Electromagnetic Induction

Read Explanation

Waves Physics

Read Explanation

Oscillations

Read Explanation

Famous Physicists

Read Explanation

Dynamics

Read Explanation

Force

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