Vibrations

Question 1

What are vibrations?

Answer 1

Vibration: a body moves back and forth about anequilibrium position

Question 2

What is a cycle?

Answer 2

A complete cycle of vibration or
oscillation means one round trip, e.g.
from X to Y and back to X again, or from
O to Y to O to X and back to O

Question 3

What is a period?

Answer 3

Time required for one cycle of the vibration. Unit in seconds (s)

Question 4

What is frequency?

Answer 4

Number of oscilliations that occur in one second

Question 5

Formula of frequency?

Answer 5

f=1/t
Frequency=1/time
Frequency in Hz.

Question 6

What is ampltiude?

Answer 6

Maximum distance from the equilibrium position

Question 7

What are typical vibration waveforms?

Answer 7

-Sawtooth wave
-Rectengular Wave
-Triangular wave
-Sinusoidal wave
-Simple Harmonic motion

Question 8

Examples of simple harmonic motion?

Answer 8

-Mass on spring, pendulum (for small angles of swing)
– Electromagnetic fields in light, radio waves
– Thermal vibration of atoms in solids
– Current and voltage in AC circuits
– Pure tone sound waves

Question 9

What is the sine function expressed as? And how to calculate displacement of a simple harmonic motion.

Answer 9

y = A sin(ωt)
Displacement (m) = Amplitude (m) x (Angular Frequency (rad s^-1 x Time (s)

Question 10

How to calculate angular frequency?

Answer 10

ω= 2 x pi x f
Angular frequency= 2 x pi x frequency

Question 12

What happens when t=0 in a simple harmonic motion?

Answer 12

Y= Ax sin (wt)
Displacement= Amplitude (m) x sin (Angular frequency (rad s^-1) x time (s))

Question 13

What does this φ symbol mean?

Answer 13

(Phi) is the initial displacement of y0 known as the phase angle

Question 14

What is the equation of SHM when phase angle is involved?

Answer 14

Will change from y=A x sin ( w x t ) to y = A sin(ωt + φ)

Question 15

How does having a phase angle effect the waveform?

Answer 15

A positive φ (phase angle), sliding to the left;
A negative φ (phase angle) sliding to the right.

Question 16

The phase difference between 2 SHMS can be found by

Answer 16

Subtract the phase angle (φ).
Ex: P lags Q by φ

Question 17

How to find the phase angle of a SHM

Answer 17

-If you know y0 and the amplitude you can use the formula:
φ=sin^01 (y0/A)
Phase angle= Inverse of sin (Displacement/Ampitude)

Question 18

How to calculate the phase angle lag of 2 SHMs if it is a cos graph

Answer 18

Since Cos graphs are ahead Pi/2 of sin. You just need to do calculate phase angle normally and add pi/2 at the end.

Question 19

How to calculate an SHM with displacements:
-Velocity
-Acceleration

Answer 19

To find the velocity, you need to differentiate the displacement:
-v= dt/dy=Aωcos(ωt+ϕ)
To find the acceleration, you need to differentiate the velocity:
-a= dt/dv=−Aω 2sin(ωt+ϕ)

Question 20

Understand slide 17

Answer 20

Please :)