Vibrations

Question 1

Define Simple Harmonic motion.

Answer 1

SHM occurs when an object moves such that its acceleration is always directed toward a fixed point and is proportional to it’s distance from the fixed point.

Question 2

What are the two conditions required for an object to undergo SHM?

Answer 2

1. Acceleration is proportional to displacement.
2. Acceleration is always directed towards a fixed point.

Question 3

When is velocity greatest in SHM?

Answer 3

When at equilibrium position

Question 4

When is velocity Least in SHM

Answer 4

When at max displacement or amplitude

Question 5

When is acceleration greatest in SHM?

Answer 5

When at max displacement or amplitude

Question 6

When is acceleration least in SHM?

Answer 6

When at equilibrium position

Question 7

What are Free oscillations

Answer 7

They are where the total energy of an oscillating system stays constant, but it’s changing between kinetic and potential energy. This is due to the oscillations being initiated and then left alone

Question 8

Damping

Answer 8

Is where an amplitude is decreasing over time due to resistive forces acting upon it

Question 9

Describe Light Damping

Answer 9

Period remains unchanged however amplitude decreases as time passes

Question 10

Describe heavy damping (or over damping)

Answer 10

When the resistive forces are significantly greater, the oscillating system will barely be able to complete one cycle.

Question 11

Describe Critical damping

Answer 11

Is where a system returns to the equilibrium in the least time possible, where the displacement never becomes negative.

Question 12

Define Natural Frequency

Answer 12

The frequency at which a system oscillates without any force applied

Question 13

Define Resonance

Answer 13

If a system is acted upon by a sinusoidally varying oscillating force it will be forced to vibrate at the forcing frequency, if the frequency is equal to the natural frequency of the system, each push will build up the amplitude further.

Question 14

What are the three effects of increasing damping on natural frequency?

Answer 14

1. The amplitude of the peak oscillation decreases
2. The resonance peak gets broader
3. The frequency at which maximum response occurs also decreases

Question 15

Displacement, (Vibrations)

Answer 15

Distance of an oscillator from its equilibrium position

Question 16

Amplitude, (Vibrations)

Answer 16

Maximum displacement of the oscillator from its equilibrium position

Question 17

What is the equation for SHM

Answer 17

a = -ω^2x

Question 18

What is the equation for maximum acceleration of an object in SHM

Answer 18

a max = -ω^2 A

Question 19

Describe an acceleration-displacement graph of an object in SHM

Answer 19

A negative straight line gradient passing through the origin.

Question 20

What is a phase angle

Answer 20

The phase difference between two oscillations

Question 21

What is the equation for maximum orbital velocity

Answer 21

v max = Aω

Question 22

What is the value of the phase difference if x = 0 when t = 0

Answer 22

ε = -pi/2

Question 23

What is the value of the phase difference if x = A when t = 0

Answer 23

ε = 0

Question 24

What is the easy way of remembering the difference between, a displacement, velocity, and acceleration graph when the object is in SHM

Answer 24

Velocity is half a phase behind Displacement, and Acceleration is another half a phase behind Velocity

Question 25

What are forced oscillations

Answer 25

Sinusoidally varying force is applied to a system to try to force it to oscillate at the frequency of the applied force.

Question 26

What is an example of a Forced oscillating system

Answer 26

An adult pushing a child on a swing set, where the adult is the force applied to the system and the swing set is the sinusoidally oscillating object