   Chapter 13, Problem 32P

Chapter
Section
Textbook Problem

A spring of negligible mass stretches 3.00 cm from its relaxed length when a force of 7.50 N is applied. A 0.500-kg particle rests on a frictionless horizontal surface and is attached to the free end of the spring. The particle is displaced from the origin to x = 5.00 cm and released from rest at t = 0. (a) What is the force constant of the spring? (b) What are the angular frequency ω, the frequency, and the period of the motion? (c) What is the total energy of the system? (d) What is the amplitude of the motion? (c) What are the maximum velocity and the maximum acceleration of the particle? (f) Determine the displacement x of the particle from the equilibrium position at t = 0.500 s. (g) Determine the velocity and acceleration of the particle when t = 0.500 s.

(a)

To determine
The force constant of the spring.

Explanation

Given info: The force applied F=7.50N . The spring is stretched to 3.00cm .

Explanation:

From the hook’s law, the restoring force is,

F=kx

• F is the restoring force
• k is the force constant of the spring
• x is the displacement from the equilibrium position

The magnitude of the force constant will be,

k=Fx

Substituting F=7.50N and x=3.00cm

k=(7

(b)

To determine
The angular frequency, the frequency, and the time period of the oscillation.

(c)

To determine
The total energy of the system.

(d)

To determine
The amplitude of the system.

(e)

To determine
The maximum velocity and the maximum acceleration of the system.

(f)

To determine
The displacement x of the particle from the equilibrium position t=0.500s .

(g)

To determine
The velocity and acceleration of the particle at t=0.500s .

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