PHYS 1511 Chapter Notes - Chapter 15: Equilibrium Point

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kiranmsubbu

21 Apr 2023

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University of Iowa

Department

Physics

Course

PHYS 1511

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Document Summary

Chapter 15 of cutnell and johnson"s "physics" textbook, 11th edition, focuses on simple harmonic motion. Simple harmonic motion is a type of motion that repeats itself over and over again in a regular pattern, and it is characterized by a restoring force that is proportional to the displacement from equilibrium. The chapter begins by introducing the concept of an oscillation, which is a back-and-forth motion around an equilibrium position. The period of an oscillation is the time it takes to complete one full cycle of motion, while the frequency is the number of cycles completed in one second. The amplitude is the maximum displacement from equilibrium. Next, the chapter discusses the different types of oscillations, including those that are damped and those that are driven. Damped oscillations decrease in amplitude over time due to the presence of friction or other forms of resistance, while driven oscillations are those that are periodically forced to oscillate.

An object of mass m attached to a spring of force constant k oscillates with simple harmonic motion. The maximum displacement from equilibrium is A and the total mechanical energy of the system is E.What is the object's velocity when its potential energy is 2/3E?

orangeswan316

Good Vibes: Introduction to Oscillations

The conditions that lead to simple harmonic motion are as follows:

There must be a position of stable equilibrium.

There must be a restoring force acting on the oscillating object. The direction of this force must always point toward the equilibrium, and its magnitude must be directly proportional to the magnitude of the object's displacement from its equilibrium position. Mathematically, the restoring force F⃗ is given by ⃗, where is the displacement from equilibrium and k is a constant that depends on the properties of the oscillating system.

The resistive forces in the system must be reasonably small.

Consider a block of mass m attached to a spring with force constant k, as shown in the figure(Figure 1) . The spring can be either stretched or compressed. The block slides on a frictionless horizontal surface, as shown. When the spring is relaxed, the block is located at x=0. If the block is pulled to the right a distance A and then released, A will be the amplitude of the resulting oscillations.

Assume that the mechanical energy of the block-spring system remains unchanged in the subsequent motion of the block.

Part A

After the block is released from x=A, it will

(a) remain at rest

(b) move to the left until it reaches equilibrium and stop there.

(d) move to the left until it reaches x=−A and then begin to move to the right.

The time it takes the block to complete one cycle is called the period. Usually, the period is denoted T and is measured in seconds.

The frequency, denoted f, is the number of cycles that are completed per unit of time: f=1/T. In SI units, f is measured in inverse seconds, or hertz (Hz).

Part B

If the period is doubled, the frequency is

(a) unchanged

(b) doubled

Part C

An oscillating object takes 0.10 s to complete one cycle; that is, its period is 0.10 s. What is its frequency f?

Express your answer in hertz.

Part D

If the frequency is 40 Hz, what is the period T?

Express your answer in seconds.

The following questions refer to the figure (Figure 2) that graphically depicts the oscillations of the block on the spring.

Note that the vertical axis represents the x-coordinate of the oscillating object, and the horizontal axis represents time.

Part E

Which points on the x-axis are located at a distance A from the equilibrium position?

(a) R only

(b) Q only

Part F

Suppose that the period is T. Which of the following points on the t-axis are separated by the time interval T?

(a) K and L

(b) K and M

(d) L and N

(e) M and P

Now assume for the remaining Parts G - J, that the x coordinate of point R is 0.12 m and the t coordinate of point K is 0.0050 s.

Part G

What is the period T?

Express your answer in seconds.

Part H

How much time t does the block take to travel from the point of maximum displacement to the opposite point of maximum displacement?

Express your answer in seconds.

Part I

What distance d does the object cover during one period of oscillation?

Express your answer in meters.

Part J

What distance d does the object cover between the moments labeled K and N on the graph?

Express your answer in meters.

emeraldyak680

An object having mass m is attached to a spring of force constant k oscillates with simple harmonic motion. The total mechanical energy of the system is E and the maximum displacement from equilibrium is A. What is the system's potential energy when its kinetic energy is equal to 3/4E?

PHYS 1511 Chapter Notes - Chapter 15: Equilibrium Point

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An object of mass m attached to a spring of force constant k oscillates with simple harmonic motion. The maximum displacement from equilibrium is A and the total mechanical energy of the system is E.What is the object's velocity when its potential energy is 2/3E?