   Chapter 13, Problem 27P

Chapter
Section
Textbook Problem

The position of an object connected to a spring varies with time according to the expression x = (5.2 cm) sin (8.07πt). Find (a) the period of this motion, (b) the frequency of the motion, (c) the amplitude of the motion, and (d) the first time after t = 0 that the object reaches the position x = 2.6 cm. constant of the springs? (b) The four people get out of the car and bounce it up and down. What is the frequency of the car’s vibration?

a)

To determine
The period of the motion.

Explanation

Given info: The position of the object varies with time t as x=(5.2cm)sin(8.0πt) .

Explanation:

The position of the object is:

x=(5.2cm)sin(8.0πt)

Here,

x is the position

t is time taken

The general expression of position as a function of time for an object moving in simple harmonic motion is given by,

x=Asin(ωt)

Here,

A is the amplitude of the simple harmonic motion

t is time taken

From the above equations,

The amplitude A=5.2cm

b)

To determine
The frequency of the motion.

c)

To determine
The amplitude of the motion.

d)

To determine
The first time the object reaches the position x=2.6cm .

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