Flashcards in 9.1 Simple Harmonic Motion Deck (15):

1

## What is simple harmonic motion?

### The acceleration and the net force are PROPORTIONAL TO and in the OPPOSITE DIRECTION to the displacement from equilibrium.

2

## What is the formula for simple harmonic motion?

###
a = -w^2x

w is constant called the angular frequency.

3

## What does SHM consist of?

### Periodic oscillations with a period that is independent of the amplitude.

4

## What is the period?

### T = 2pi/w

5

## What is the phase?

### An angle added to wt in the formulas for x,v and a which indicates their values at t=0.

6

## What is the formula for potential energy?

### Ep = 1/2mw^2x^2

7

## What is the formula for kinetic energy?

### Ek = 1/2mw^2(x0^2-x^2)

8

## What are the two special cases of SHM?

###
A mass m at the end of a spring with spring constant k the period T = 2pi sqr rt(m/k)

A single pendulum of length l the period is

T = 2pi sqr rt(l/g)

9

## What is important about the period expression for the pendulum?

### The expression for the pendulum is true provided the amplitude is small. Note that the period of a pendulum does not depend on its mass.

10

## Why is common choice of phase 0?

###
Since x = x0coswt

v = -wx0sinwt

a = -w^2xocoswt

The maximum speed is v max = wx0

the maximum acceleration is a max = w^2x0

11

##
Why is another common choice of phase

- pi/2

###
x = x0sinwt

v = wx0coswt

a = -w^2x0sinwt

12

## What happens to the kinetic and potential energy in SHM?

### They are constantly transferred into one another.

13

## When does the maximum potential energy occur?

### 1/2mw^2x0^2 occurs at maximum displacement where the speed is 0. Therefore the kinetic energy is also zero at this point so the formula above is a measure of the total energy.

14

## How is the kinetic energy at any displacement given?

###
Since ET = EK + EP at any point the keitnc energy at any displacement is given by

1/2mv^2 = 1/2mw^2x0^2 - 1/2mw^2x^2

so v = plus or minus w times sqr rt(x0^2 - x^2)

15