PHYS 2211 Lecture Notes - Lecture 8: Angular Frequency, Stopwatch, List Of Trigonometric Identities

15 views6 pages

burgundyhound215

30 Mar 2019

School

Department

Course

Professor

For unlimited access to Class Notes, a Class+ subscription is required.

Document Summary

In the last unit on classical mechanics we consider a special type of motion known as harmonic motion . This type of motion is distinct because of the repetitive nature. Consider a ball on a spring that bounces up and down or a child on a swing that goes back and forth. We will take the same approach with this unit that we did with all of mechanics. We will look at the motion, then forces that cause the motion and finally the energy of a vibrating system. How fast an object or system oscillates or vibrates can be described in any of three ways. This is a question of time and is measured in seconds. We wish to use the letter t for time but this is a special time so we use tau. This is the inverse of the last question.

Related Questions

14.1. BIO (a) Music. When a person sings, his or her vocal cords vibrate in a repetitive pattern that has the same frequency as the note that is sung. If someone sings the note B flat, which has a frequency of 466 Hz, how much time does it take the person's vocal cords to vibrate through one complete cycle, and what is the angular frequency of the cords? (b) Hearing. When sound waves strike the eardrum, this membrane vibrates with the same frequency as the sound. The highest pitch that young humans can hear has a period of 50.0 us. What are the frequency and angu- lar frequency of the vibrating eardrum for this sound? (c) Vision. When light having vibrations with angular frequency ranging from 2.7 X 10" rad/s to 4.7 x 101 rad/s strikes the retina of the eye, it stimulates the receptor cells there and is perceived as vis- ible light. What are the limits of the period and frequency of this light? (d) Ultrasound. High-frequency sound waves (ultrasound) are used to probe the interior of the body, much as x rays do. To detect small objects such as tumors, a frequency of around 5.0 MHz is used. What are the period and angular frequency of the molecu- lar vibrations caused by this pulse of sound?

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

PHYS 2211 Lecture Notes - Lecture 8: Angular Frequency, Stopwatch, List Of Trigonometric Identities

Document Summary

Get access

Related textbook solutions

Physics: Principles with Applications

Related Documents

PHYS 2211 Lecture Notes - Lecture 5: Angular Velocity, Speed, Angular Frequency

PHYS 2211 Lecture Notes - Lecture 9: Transverse Wave, Longitudinal Wave, Standing Wave

PHYS 2211 Study Guide - Midterm Guide: Acceleration, Centripetal Force, Centrifugal Force

Related Questions