Simple Harmonic Motion

Question 1

What is simple harmonic motion?

Answer 1

Simple harmonic motion is a type of motion that occurs when acceleration is directly proportional to the displacement from a fixed point, and is always in the direction of that fixed point.

Question 2

What are the 2 requirements for a body to be in simple harmonic motion?

Answer 2

1) The acceleration of the body is always directed to the fixed point
2) The acceleration of the body is directly proportional to the displacement from the fixed point

Question 3

What is the equation of simple harmonic motion?

Answer 3

a = -ω^2x

Question 4

As a body is in SHM when does it’s acceleration increase?

Answer 4

When it’s displacement from the equilibrium position increases.

Question 5

As a body is in SHM when does it’s velocity increase?

Answer 5

When it’s displacement from the equilibrium position decreases.

Question 6

What is the equation for displacement of a body in SHM starting at the extremity?

Answer 6

x = Acos(ωt)

Question 7

What is the equation for displacement of a body in SHM starting at the equilibrium?

Answer 7

x = Asin(ωt)

Question 8

How is velocity found using the equations of displacement?

Answer 8

But differentiating the displacement equation

Question 9

What is the equation of maximum velocity?

Answer 9

V = Aω

Question 10

What is the equation of finding the period of the mass in a spring?

Answer 10

T = 2π√m/k

Question 11

What is the equation for the period in a pendulum?

Answer 11

T = 2π√l/g

Question 12

What is the energy equation for maximum KE?

Answer 12

kE = (1/2)m(ωA)^2

Question 13

What is the energy relation in oscillation?

Answer 13

As the body moves towards the extremity, it’s potential energy increase whereas it’s kinetic energy decreases. However as the body moves towards equilibrium it’s potential energy decreases and its kinetic energy increases. Within SHM this conversion of energy is constantly occurring.

Question 14

What are free oscillations?

Answer 14

Free oscillations are oscillations which are unaffected by external forces or actions as there are no dissipative forces acting on them causing their amplitude to be consistent

Question 15

What are forced oscillations?

Answer 15

Forced oscillations are are oscillations produced by the action of a periodic driving force

Question 16

What is damping?

Answer 16

Damping means that the total energy of the oscillation is being reduced and this is done by resistive forces that are in the opposite direction. They cause energy to be absorbed from the system.

Question 17

What is light damping?

Answer 17

Light damping is where the energy of the system gradually decreases overtime therefore the amplitude decreases overtime and the period is unaffected

Question 18

What is heavy damping?

Answer 18

Heavy damping is where a system is set into oscillation but takes a long time to return to equilibrium, and it will never complete a full oscillation

Question 19

What is critical damping?

Answer 19

Critical damping is when a system is displaced but not set into oscillation and returns to equilibrium in a quarter of a period with no or little overshoot

Question 20

Where is critical damping used?

Answer 20

In car systems or bike suspensions

Question 21

What is resonance?

Answer 21

Resonance is when the frequency of the driving force matches the natural frequency of the system causing the system to absorb energy and therefore creating a maximum in the amplitude of oscillation

Question 22

Where is resonance useful?

Answer 22

In microwaves, as the frequency of the microwave is similar to the natural frequency of the water molecules allowing food to heat up

Question 23

Where is resonance useless?

Answer 23

On bridges, as if the frequency of people walking matches the natural frequency of the bridge, it can cause the bridge to oscillate too much

Question 24

What is the effect of damping on natural frequency?

Answer 24

• The amplitude of peak oscillation decreases (effect decreases further away from resonance)
• The resonance peak gets broader
• The frequency as which maximum response occurs also decreases