Ch 14: Periodic Motion

Question 1

A body that undergoes periodic motion always has _____.

Answer 1

a stable equilibrium postion

Question 2

Why does a body moved away from its equilibrium position overshoot the equilibrium position when released?

Answer 2

It has picked up some kinetic energy

Question 3

In SHM, it’s simplest to define _____ as the origin.

Answer 3

the equilibrium postion

Question 4

Whenever a body is displaced from its equilibrium position, the spring force _____. This is called _____.

Answer 4

tends to restore it to the equilibrium position; a restoring force

Question 5

Oscillation can occur only when there is _____.

Answer 5

a restoring force tending to return the system to equilibrium

Question 6

In SHM, when the body is at O, the net force acting on it is _____.

Answer 6

zero

Question 7

When the body is to the left/right of equilibrium, the net force and acceleration are to the _____.

Answer 7

right/left

Question 8

amplitude, A

Answer 8

the maximum magnitude of displacement from equilibrium; always positive

Question 9

What is one cycle (give an example)?

Answer 9

one complete round trip: for example, from A to -A and back to A, or from O to A back to O to -A back to O

Question 10

period, T

Answer 10

the time for one cycle; always positive; measured in cycles per second

Question 11

frequency, f

Answer 11

number of cycles per unit time; measured in Hz

Question 12

angular frequency, ω?

Answer 12

rate of change of an angular quantitiy (not necessarily related to a rotational motion); 2πf; measured in rad/s

Question 13

How is ω related to T?

Answer 13

ω= 2πf = 2π/T

Question 14

When does the simplest kind of oscillation occur and what is this called?

Answer 14

when the restoring force is directly proportional to the displacement from equilibrium; this is called simple harmonic motion

Question 15

Hooke’s Law

Answer 15

F = -kx

Question 16

What is the acceleration of a body in SHM?

Answer 16

-(kx)/m

Question 17

In SHM, acceleration and displacement always have _____.

Answer 17

opposite signs

Question 18

T/F: Acceleration in SHM is constant.

Answer 18

Wicked, tricksy, FALSE!

Question 19

SHM is the projection of _____.

Answer 19

uniform circular motion onto a diameter

Question 20

phasor

Answer 20

a rotating vector

Question 21

What is the value of the x-component of the phasor at time t?

Answer 21

x=Acosθ

Question 22

How is ω related to k and m?

Answer 22

ω = √(k/m)

Question 23

In simple harmonic motion, the period and frequency do not depend on _____.

Answer 23

amplitude

Question 24

What is the equation for displacement in SHM?

Answer 24

x=Acos(ωt + Φ)

Question 25

What are the max and min values of x in SHM?

Answer 25

-A and A

Question 26

Changing m or k changes _____.

Answer 26

the period of oscillation

Question 27

phase angle, Φ

Answer 27

tells at what point in the cycle the motion was at t=0

Question 28

If Φ=0, then x_0=

Answer 28

A, and the body starts at its max positive displacement

Question 29

If Φ=π, then x_0=

Answer 29

-A, and the body starts at is max negative displacement

Question 30

How is v_0 related to ω, A, and Φ?

Answer 30

v_0 = -ωAsinΦ

Question 31

What is the equation for Φ?

Answer 31

Φ = arctan( - v_0/ωx_0)

Question 32

What is the equation for A?

Answer 32

√(x_0^2 +v_0^2/ω^2)

Question 33

When the body has both an initial displacement and a nonzero initial velocity, the amplitude is ______.

Answer 33

NOT equal to the initial displacement

Question 34

What is total mechanical energy equal to in SHM?

Answer 34

E = ½mv^2 + ½kx^2 = ½kA^2 = constant

Question 35

The velocity of a body in SHM is _____.

Answer 35

not constant

Question 36

At x = ± A, the energy is all ______.

Answer 36

potential

Question 37

T/F: There are major differences between vertical SHM and horizontal SHM.

Answer 37

FALSIES

Question 38

When a body is hanging from a vertical spring in equilibrium, _____ is equal to _____.

Answer 38

the spring's upward vertical force; the body's weight; kΔl = mg

Question 39

What is the only difference between vertical and horizontal SHM?

Answer 39

In vertical SHM, the equilibrium position x=0 no longer corresponds to the point at which the spring is unstretched

Question 40

Describe angular SHM in a mechanical watch.

Answer 40

The wheel has a moment of inertia about its axis and the coil spring exerts a torque proportional to the angular displacement from equilibrium

Question 41

What is ω equal to in angular SHM?

Answer 41

ω=√(κ/I)

Question 42

What is the equation for displacement in angular SHM?

Answer 42

θ=Θcos(ωt +Φ)

Question 43

Is the system of two atoms fundamentally different from a mass attached to a horizontal spring?

Answer 43

NOPE NOPE NOPE

Question 44

What is a simple pendulum?

Answer 44

A point mass suspended by a massless, unstretchable string

Question 45

What is the restoring force for a simple pendulum and what is it provided by?

Answer 45

F= -mgsinθ ; gravity

Question 46

What is ω for a simple pendulum?

Answer 46

√(g/L)

Question 47

What is a physical pendulum?

Answer 47

Any pendulum that uses an extended body

Question 48

In the equilibrium position, the center of gravity of a physical pendulum is _____.

Answer 48

directly below the pivot point

Question 49

When a physical pendulum is displaced from equilibrium by θ, the weight causes a restoring torque equal to _____.

Answer 49

-mgdsinθ, where d is the length from the pivot point to the center of equilibrium

Question 50

If θ is small, we can make the approximation that _____.

Answer 50

sin θ = θ in radians, so τ = -mgdθ

Question 51

What is ω for a physical pendulum?

Answer 51

√(mgd/I)

Question 52

damping

Answer 52

the decrease in amplitude caused by dissipative forces

Question 53

What is the net force on a body going under damped oscillation?

Answer 53

ΣF= -kx - bv

Question 54

What is the displacement for a body going under damped oscillation?

Answer 54

x = Ae^[-(b/2m)t] cost ( ω't + Φ)

Question 55

What is the angular frequency for a body going under damped oscillation?

Answer 55

√(k/m - b^2/4m^2)

Question 56

critical damping

Answer 56

when angular frequency is equal to zero; b = 2√(km); the system no longer oscillates but returns to its equilibrium position

Question 57

overdamping

Answer 57

b > 2√(km) ; no oscillation, system returns to equilibrium more slowly

Question 58

underdamping

Answer 58

b < 2√(km) ; system oscillates with steadily decreasing amplitude