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Physics 1B > Ch 14: Periodic Motion > Flashcards

Ch 14: Periodic Motion Flashcards

1
Q

A body that undergoes periodic motion always has _____.

A

a stable equilibrium postion

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2
Q

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

A

It has picked up some kinetic energy

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3
Q

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

A

the equilibrium postion

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4
Q

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

A

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

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5
Q

Oscillation can occur only when there is _____.

A

a restoring force tending to return the system to equilibrium

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6
Q

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

A

zero

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7
Q

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

A

right/left

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8
Q

amplitude, A

A

the maximum magnitude of displacement from equilibrium; always positive

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9
Q

What is one cycle (give an example)?

A

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

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10
Q

period, T

A

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

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11
Q

frequency, f

A

number of cycles per unit time; measured in Hz

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12
Q

angular frequency, ω?

A

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

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13
Q

How is ω related to T?

A

ω= 2πf = 2π/T

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14
Q

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

A

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

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15
Q

Hooke’s Law

A

F = -kx

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16
Q

What is the acceleration of a body in SHM?

A

-(kx)/m

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17
Q

In SHM, acceleration and displacement always have _____.

A

opposite signs

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18
Q

T/F: Acceleration in SHM is constant.

A

Wicked, tricksy, FALSE!

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19
Q

SHM is the projection of _____.

A

uniform circular motion onto a diameter

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20
Q

phasor

A

a rotating vector

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21
Q

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

A

x=Acosθ

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22
Q

How is ω related to k and m?

A

ω = √(k/m)

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23
Q

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

A

amplitude

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24
Q

What is the equation for displacement in SHM?

A

x=Acos(ωt + Φ)

25
Q

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

A

-A and A

26
Q

Changing m or k changes _____.

A

the period of oscillation

27
Q

phase angle, Φ

A

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

28
Q

If Φ=0, then x_0=

A

A, and the body starts at its max positive displacement

29
Q

If Φ=π, then x_0=

A

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

30
Q

How is v_0 related to ω, A, and Φ?

A

v_0 = -ωAsinΦ

31
Q

What is the equation for Φ?

A

Φ = arctan( - v_0/ωx_0)

32
Q

What is the equation for A?

A

√(x_0^2 +v_0^2/ω^2)

33
Q

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

A

NOT equal to the initial displacement

34
Q

What is total mechanical energy equal to in SHM?

A

E = ½mv^2 + ½kx^2 = ½kA^2 = constant

35
Q

The velocity of a body in SHM is _____.

A

not constant

36
Q

At x = ± A, the energy is all ______.

A

potential

37
Q

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

A

FALSIES

38
Q

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

A

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

39
Q

What is the only difference between vertical and horizontal SHM?

A

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

40
Q

Describe angular SHM in a mechanical watch.

A

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

41
Q

What is ω equal to in angular SHM?

A

ω=√(κ/I)

42
Q

What is the equation for displacement in angular SHM?

A

θ=Θcos(ωt +Φ)

43
Q

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

A

NOPE NOPE NOPE

44
Q

What is a simple pendulum?

A

A point mass suspended by a massless, unstretchable string

45
Q

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

A

F= -mgsinθ ; gravity

46
Q

What is ω for a simple pendulum?

A

√(g/L)

47
Q

What is a physical pendulum?

A

Any pendulum that uses an extended body

48
Q

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

A

directly below the pivot point

49
Q

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

A

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

50
Q

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

A

sin θ = θ in radians, so τ = -mgdθ

51
Q

What is ω for a physical pendulum?

A

√(mgd/I)

52
Q

damping

A

the decrease in amplitude caused by dissipative forces

53
Q

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

A

ΣF= -kx - bv

54
Q

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

A

x = Ae^[-(b/2m)t] cost ( ω’t + Φ)

55
Q

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

A

√(k/m - b^2/4m^2)

56
Q

critical damping

A

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

57
Q

overdamping

A

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

58
Q

underdamping

A

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

Physics 1B (7 decks)

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