9.1 Simple Harmonic Motion Flashcards Preview

Physics Chapter 9 - Wave Phenomena > 9.1 Simple Harmonic Motion > Flashcards

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

What happens as the oscillating body goes past the equilibrium point?

displacement is zero and so the velocity is equal to plus or minus wx0.