   Chapter 13, Problem 29P

Chapter
Section
Textbook Problem

A 326-g object is attached to a spring and executes simple harmonic motion with a period of 0.250 s. If the total energy of the system is 5.83 J, find (a) the maximum speed of the object, (b) the force constant of the spring, and (c) the amplitude of the motion.

a)

To determine
The maximum speed of the object executing simple harmonic motion.

Explanation

Given info: The mass of the object is 326g . The period of the simple harmonic motion is 0.250s . The total energy of the system is 5.83J .

Explanation:

When the system is in its equilibrium position, the total energy is stored as kinetic energy.

E=12mvmax2

Here,

E is the total energy

m is the mass of the object

vmax is the maximum velocity of the object

Re-arranging for vmax

vmax=2Em

Substituting m=326g and E=5

b)

To determine
The force constant of the spring.

c)

To determine
The amplitude of the simple harmonic motion.

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