Simple Harmonic Motion

Question 1

Simple Harmonic Motion

Answer 1

a type of periodic motion in which the acceleration is - - proportional to the displacement from the equilibrium position
- directed towards the equilibrium point

a ∝ - s
a = - w²s
( if there is an a there is an F)

Question 2

Hooke’s Law

Answer 2

F ∝ - s
- whenever an object is deformed through bending, stretching or compression there is a resisting force which is perpendicular to the displacement and acts in the opposite direction to it, so long as the elastic limit is not exceeded

Question 3

Hooke’s Law Equation

Answer 3

F = - ks
k = elastic constant (different for every material)
s = displacement from the original shape (m)
F = restoring force (N)

Question 4

Periodic Motion

Answer 4

motion that is
-  regular and repeating
- can be predicted 
- follow the same set path over and over
(follows a definite periodic pattern)

• e.g tidal motion, pendulum motion

Question 5

SHM formula for acceleration

Answer 5

a ∝ - s
a = - w²s

• acceleration always points to equilibrium
• string stretched out of equilibrium will move up with restoring force ∝ to displacement from the equilibrium which causes it to accelerate and move past equilibrium due to momentum
• as soon as object passes equilibrium point it starts to slow down - a decreases

Question 6

equillibrium

Answer 6

where a spring would naturally rest

Question 7

damping

Answer 7

an effect that reduces the amplitude in an oscillatory system

• air resistance
• gravity
• friction

Question 8

Derivation of a = - w²s

Answer 8

from hooke's law 
1) F = - ks 
sine F = ma 
2)  - ks = ma 
3)   -ks/m = a
let w² = k/m
4)  - w²s = a

Question 9

oscillating

Answer 9

to swing back and forth with a steady rhythm

Question 10

cycle

Answer 10

the full range of movement from one extreme to another and back again

Question 11

frequency

Answer 11

number of cycle that can happen each second

Question 12

period (T)

Answer 12

the time taken to complete one cycle (one full revolution)

Question 13

amplitude

Answer 13

the displacement from the equilibrium point to the max/min point

Question 14

Periodic Time

Answer 14

T = 1/f ( frequency of oscillation)

T = 2π/w

Question 15

Periodic time for a pendulum

Answer 15

T = 2π√l/g

!! for angles < 5° !!

T = periodic time (seconds)
l = length of pendulum from point of suspension to centre of mass (m) !!
g = acceleration due to gravity (m/s²)

Question 16

Energy transfer in SHM

Answer 16

• oscillation converts energy (Ep - Ek - Ep)
• continues until mass is at rest at equilibrium (due to damping)

At max/ min point
a = max 
v = min (0)
Ep = max
Ek = min (0)

At equilibrium point
a = min (0)
v = max 
Ep = min (0)
Ek = max

Question 17

Pendulum experiment `

Answer 17

• x = T²
• y = l
• slope = g/4π

so slope x 4π = g

• measure t 20
• divide by 20 to get T
• split cork
• measure l from point of suspension to the centre of the bob mass
• length of string < 40 cm
• angle < 5° (air resistance)