Chapter 4: Q51P (page 168)

A mass of $2.2 k g$ is connected to a horizontal spring whose stiffness is role="math" localid="1657769591862" $8 N / m$ . When the spring is relaxed, $x = 0 .$ The spring is stretched so that the initial value of $x = + 0.18 m$ . The mass is released from rest at time role="math" localid="1657769734196" $t = 0$ . Remember that when the argument of a trigonometric function is in radians, on a calculator you have to switch the calculator to radians or convert the radians to degrees. Predict the position x when $t = 1.15 s$ .

Short Answer

Expert verified

The displacement of spring is $x = - 0.1049 m$ when at $t = 1.15 s$ .

Step by step solution

Identification of given data

Given data can be listed below,

Mass, $m = 2.2 k g$
Spring stiffness, $k = 8 N / m$
Displacement of spring, $x = 0.18 m$

Evaluating the angular frequency of the spring-mass system

Expression for angular frequency of the spring-mass system is given by

$ω = \sqrt{\frac{k}{m}} = \sqrt{\frac{8}{2.2}} = 1.907 r a d / s$

Displacement of spring when t=1.15 m

Expression for analytical solution for spring-mass system is given by

$ω t = A \cos ()$

The spring is stretched initial value of $x = 0.18 m$ When time $t = 0$

Substituting $x = 1.18 m$ and $t = 0$ in the above equation we get

$0.18 = A \cos (1.09 \times 0) 0.18 = A A = 0.18 m W h e n t = 1.15 s x = 0.18 \cos (1.907 r a d \times \frac{180^{0}}{π} \times 1.15 s) = - 0.1049 m$

Thus, the displacement of spring $x = - 0.1049 m$ when $t = 1.15 s$

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!

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Short Answer

Step by step solution

Identification of given data

Evaluating the angular frequency of the spring-mass system

Displacement of spring when t=1.15 m

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Further Mechanics and Thermal Physics

Electricity and Magnetism

Force

Astrophysics

Engineering Physics

Quantum Physics

Study anywhere. Anytime. Across all devices.