Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 15: Q32P (page 437)

Figure shows the kinetic energy Kof a simple harmonic oscillator versus its position . The vertical axis scale is set by Ks=4.0J. What is the spring constant?

Short Answer

Expert verified

The spring constant of a simple harmonic oscillator is 8.33×102N/m.

Step by step solution

01

The given data

From graph, we can say that,

  1. Total energy of the system E = 6.0 J,
  2. The amplitude of the oscillation, Xm=12cmor0.12m.
02

Understanding the concept of motion

Using the given graph we can find the total energy and amplitude of motion, so we can find the spring constant.

Formula:

The energy of the system of the harmonic oscillator,

E=12kxm2...(1)

03

Calculation of spring constant

Using equation (i) and the given values, we get the spring constant as given:

6.012k(0.12)2k=8.33×102N/m

The value of the spring constant is8.33×102N/m .

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

What is the length of a simple pendulum whose full swing from left to right and then back again takes 3.2 S?

A flat uniform circular disk has a mass of 3.00kgand a radius of 70.0cm. It is suspended in a horizontal plane by a vertical wire attached to its center. If the disk is rotated 2.50 radabout the wire, a torque of 0.600 N.mis required to maintain that orientation.

  1. Calculate the rotational inertia of the disk about the wire.
  2. Calculate the torsion constant.
  3. Calculate the angular frequency of this torsion pendulum when it is set oscillating.

When the displacement in SHM is one-half the amplitude Xm,

  1. What fraction of the total energy is kinetic energy?
  2. What fraction of the total energy is potential energy?
  3. At what displacement, in terms of the amplitude, is the energy of the system half kinetic energy and half potential energy?

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?

The scale of a spring balance that reads from 0to 15.0 kgis12.0cm long. A package suspended from the balance is found to oscillate vertically with a frequency of 2.00 Hz.

  1. What is the spring constant?
  2. How much does the package weigh?
See all solutions

Recommended explanations on Physics Textbooks

Waves Physics

Read Explanation

Modern Physics

Read Explanation

Medical Physics

Read Explanation

Classical Mechanics

Read Explanation

Physics of Motion

Read Explanation

Energy Physics

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