13p2 Oscillations

Question 1

What is the condition for simple harmonic motion (SHM)?

Answer 1

SHM occurs when there is a restoring force that is directly proportional to displacement and directed towards the equilibrium position

Question 2

What is the formula for the restoring force in SHM?

Answer 2

F = -kx where F is the restoring force k is a system constant and x is displacement

Question 3

What does the constant k represent in SHM?

Answer 3

The constant k represents the stiffness of the system such as the spring constant in a spring

Question 4

What is amplitude in SHM?

Answer 4

Amplitude is the maximum displacement from the equilibrium position during oscillations

Question 5

What is the time period (T) of an oscillation?

Answer 5

Time period is the time taken for one complete oscillation of the system

Question 6

What is the restoring force in a simple pendulum?

Answer 6

The restoring force is the horizontal component of gravity acting on the pendulum bob

Question 7

in SHM equations, what does A, ω, x, v and a mean with units

Answer 7

A - amplitude of oscillation (m)
ω - angular frequency (rad/s)
x - displacement from equilibrium position (m)
v - velocity (m/s)
a - acceleration (m/s^2)

Question 8

What does T, l, g, m and k mean in simple harmonic oscillator questions with units

Answer 8

T - time period (s)
l - length of the pendulum (m)
g - gravitational acceleration (m/s^2)
m - mass (kg)
k - spring constant (N/m)

Question 9

What does a displacement-time graph for SHM look like?

Answer 9

A sine or cosine wave with amplitude A and period T

Question 10

How is velocity related to displacement in SHM?

Answer 10

Velocity is the gradient of the displacement-time graph and is maximum at equilibrium

Question 11

When is velocity maximum in SHM?

Answer 11

Velocity is maximum when displacement is zero which is at the equilibrium position

Question 12

What does a velocity-time graph look like in SHM?

Answer 12

A sine wave that is out of phase with displacement and peaks when displacement is zero

Question 13

How is acceleration related to displacement in SHM?

Answer 13

Acceleration is directly proportional to the negative of displacement showing a restoring force

Question 14

What is resonance?

Answer 14

Resonance is when a system is driven at its natural frequency causing a large increase in amplitude so when the driving frequency is equal to the natural frequency of the system

Question 15

Give an example of resonance in real life.

Answer 15

Swinging on a swing when pushed at the right frequency, musical instruments and radios

Question 16

What is the driving frequency?

Answer 16

The driving frequency is the frequency of the external force applied to the oscillating system

Question 17

What is damping?

Answer 17

Damping is the loss of energy from an oscillating system due to resistive forces reducing amplitude over time

Question 18

How does energy transform in SHM?

Answer 18

Energy transforms between kinetic and potential forms with total energy remaining constant in undamped systems

Question 19

What is an undamped system?

Answer 19

An undamped system has no energy loss so amplitude and total mechanical energy stay constant

Question 20

What is a damped system?

Answer 20

A damped system experiences energy loss to the environment resulting in decreasing amplitude

Question 21

What are free vibrations?

Answer 21

Free vibrations occur when a system oscillates at its natural frequency without continuous external force

Question 22

What are forced vibrations?

Answer 22

Forced vibrations occur when a system is driven by an external periodic force

Question 23

What happens when driving frequency equals natural frequency?

Answer 23

Resonance occurs and the system’s amplitude becomes very large

Question 24

What are the three types of damping?

Answer 24

Light damping critical damping and heavy damping each reducing amplitude differently

Question 25

What is light damping?

Answer 25

Light damping or underdamping is when amplitude decreases slowly with each oscillation

Question 26

What is critical damping?

Answer 26

Critical damping brings the system to rest in the shortest time without oscillating

Question 27

What is heavy damping?

Answer 27

Heavy damping or overdamping slows the return to equilibrium without oscillations and takes longer than critical damping

Question 28

How does damping affect resonance?

Answer 28

Damping lowers the resonant frequency reduces maximum amplitude and broadens the resonance curve

Question 29

What is ζ (zeta) in damping?

Answer 29

Zeta is the damping ratio with ζ = 1 indicating critical damping less than 1 is underdamped and greater than 1 is overdamped

Question 30

How do ductile materials reduce oscillation amplitude?

Answer 30

Ductile materials absorb energy through plastic deformation which reduces kinetic energy and amplitude

Question 31

Why are climbing ropes designed to be ductile?

Answer 31

Climbing ropes deform plastically to absorb energy and critically damp oscillations for safety during a fall

Question 32

Can a climbing rope be reused after a fall?

Answer 32

No because the plastic deformation permanently damages the rope's structure making it unsafe

Question 33

How to determine the value of an unknown mass using the resonant frequencies of the oscillation of known masses

Answer 33

1) hang a number of masses to the end of a spring 2) extend the spring up to the position of the fiducial marker - release it and start the stopwatch 3) measure time for 10 oscillations, use fiducial mark on clamp stand to improve accuracy 4) repeat process several times and find mean time period 5) vary number of masses and record time period for each condition 6) T^2 (y axis) against mass and draw line with best fit since t^2 = m(k/4pi^2) so t^2 is proportional to m 7) attach an unknown mass to the end of spring and record time period then use graph to find mass

Question 34

In the experiment to determine the value of an unknown mass using the resonant frequencies of the oscillation of known masses, how are errors reduced

Answer 34

finding 10 oscillations then dividing by 10 reduces percentage uncertainty use a vernier motion tracker and data logger to find a more accurate value for time period removing human error and parallax error from fiducial mark