   Chapter 13, Problem 31P

Chapter
Section
Textbook Problem

A 2.00-kg object on a frictionless horizontal track is attached to the end of a horizontal spring whose force constant is 5.00 N/m. The object is displaced 3.00 m to the right from its equilibrium position and then released, initiating simple harmonic motion. (a) What is the force (magnitude and direction) acting on the object 3.50 s after it is released? (b) How many times does the object oscillate in 3.50 s?

(a)

To determine
The force acting on the object.

Explanation

Given info: The mass of the object is m=2.00kg . Force constant of the horizontal spring is k=5.00Nm-1 . The object was displaced A=3.00m from equilibrium position towards right and released. Time t=3.50s .

Explanation:

The general expression for the simple harmonic motion of the system starting from A at t=0 is,

x=Acos(ωt)

The restoring force from hook’s law is,

F=kAcos(ωt) (3)

The angular frequency of the oscillation is defined by,

ω=km (4)

• ω is the angular frequency
• k is the force constant of the spring
• m is the mass of the object

Therefore,

F=kAcos(kmt) (5)

Substituting k=5

(b)

To determine
The number of oscillation in 3.5s .

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