Chapter 17 - Oscillations

Question 1

What is SHM

Answer 1

The motion of a body about an equilibrium point, where the acceleration is proportional to the displacement in the opposite direction.

Question 2

What is Harmonic Motion

Answer 2

A body performs a periodic motion about an equilibrium point.

An acceleration must continually act towards the equilibrium position and continually vary in size and position.

Question 3

What is the simplest way that harmonic motion can be act?

Answer 3

For the acceleration (resultant force) to be proportional to the displacement and in the opposite direction to.

Question 4

Displacement expression force and displacement

Answer 4

F= - kx

proportional and opposite direction

Question 5

Displacement expression : differential equation

Answer 5

x= A sin(wt)
x= A cos(wt)

Question 6

Differential equations: Velocity

Answer 6

v= -(Aw) sin (wt)

Question 7

When sin(wt) = +- 1, get the differential equation for Maximum velocity

Answer 7

V= +- w (A^2 -x^2)^1/2

Question 8

Differential equations: Acceleration

Answer 8

a= -(Aw^2)cos(wt)

Question 9

When cos(wt) = +- 1, get the differential equation for maximum acceleration
(x= A cos(wt))

Answer 9

a= -w^2x

Question 10

What is acceleration at its maximum

Answer 10

W^2 A

Question 11

What is velocity at its maximum

Answer 11

w A

Question 12

Why is the motion of a mass on a spring defined as being SHM

Answer 12

When the spring is displace from equilibrium, a restoring force, F will act (F= -kx) , where k is the spring constant. This force is proportional to the displacement from equilibrium, but opposite in direction.

By Newton’s 2 Law, the acceleration experience by the spring is always proportional to the displacement and in the opposite direction to.

SHM is defined as the periodic motion of a body where its restoring force is proportional t the displacement and in the opposite direction to.

Question 13

What is a damped oscillating system

Answer 13

One that is subject to an external force, they act to take energy out of a system.

Question 14

What is Light damping

Answer 14

The amplitude will gradually decrease by the same fraction every oscillation.
The period T of oscillation remains unchanged.

Question 15

What is Critical Damping

Answer 15

There’s a large external force acting on the system.
Stops the system from oscillating after it has been displaced from equilibrium.
Tries to get the system to eq. as quickly as possible.
Period of T is likely to change

Question 16

What is Heavy Damping

Answer 16

Too much external force acts.
Very strong damping and the system return to equilibrium very slowly.
Period T of oscillation is hugely increased.

Question 17

What is Natural Frequency

Answer 17

The frequency with which a system exhibiting SHM oscillated with no external force is applied to it.
There must still be an accelerating force.

Question 18

What is forced oscillations

Answer 18

Oscillating that occur when a periodic force is applied to a system exhibiting SHM.

Question 19

What is a periodic force

Answer 19

apply, dont apply, apply, don’t apply etc.

Question 20

What is resonance

Answer 20

The physical phenomena where the amplitude of an oscillating system grows rapidly occurring when the frequency of the applied periodic force matches the natural frequency of the system.

Question 21

What is a free oscillation

Answer 21

It oscillated with constant amplitude, there are no external forces that act to transfer energy out of the system.
The total energy remains constant and transfer continually between kinetic energy and potential energy.

Question 22

What energies are used in a mass-spring-system in the horizontal plane

Answer 22

Kinetic energy and elastic potential energy.

Question 23

What energies are used in a pendulum

Answer 23

Kinetic energy to gravitational potential energy

Question 24

Equation for finding the Kinetic energy at any point

Answer 24

Ek = 1/2 k (A^2 -x^2)

Question 25

Equation for finding the velocity at any given time

Answer 25

v= ((k/m)(A^2 - x^2))^1/2

Question 26

How does KE change over amplitude

Answer 26

Upside down U.

Question 27

How does PE change over amplitude

Answer 27

U.