Physics 1401A/B Lecture Notes - Lecture 10: Simple Harmonic Motion, Elastic Energy, Perpetual Motion

54 views1 pages

scarlethound445

2 Jan 2019

School

Department

Course

Professor

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

Document Summary

Elastic potential energy ideal spring and the spring"s displacement. Ideal spring: any spring that obeys hooke"s law; it does not experience any internal or external friction. Hooke"s law: the amount of force exerted by a spring is directly proportional to the displacement of the spring force exerted by the spring on whatever stretches it: displacement of the spring from its upstretched, equilibrium position. Spring constant ( ): the constant of variation between the force exerted by an. Amplitude ( ): the maximum displacement of a wave. Elastic potential energy: potential energy due to the stretching or compressing of an elastic material. Simple harmonic motion: periodic motion in which the acceleration of the moving object is proportional to its displacement. Perpetual motion: machine a machine that can operate forever without restarting or refueling. Damped harmonic motion: periodic motion affected by friction.

Related Questions

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

Physics 1401A/B Lecture Notes - Lecture 10: Simple Harmonic Motion, Elastic Energy, Perpetual Motion

Document Summary

Get access

Related textbook solutions

Physics: Principles with Applications

Related Documents

PHYS 101 Lecture Notes - Fundamental Frequency, Standing Wave, Particle Velocity

PHYS 2001 Lecture : Chap 11 Notes

PHYS 117 Chapter Notes - Chapter 13: Superposition Principle, Linear Density, Soliton

Related Questions