Simple Harmonic Motion Flashcards
describe the forces in a string when pendulum is at rest position
- resultant force is zero
- tension is upwards and equal to the weight
describe the resultant force when pendulum is oscillating
always acts towards equilibrium position (rest position)
describe the conditions needed for SHM
- acceleration is proportional to displacement from fixed point*
- direction of acceleration always towards fixed point
*cannot use newtons laws as a varies with s
what does the minus sign in the acceleration equation mean
displacement and acceleration are in opposite directions
force equation
F = ma
∴
F = -mω²𝑥
displacement-time graph
𝑥 = A cos ωt and +ve
∴
starts at max displacement and top half
top sin, bottom cos
velocity-time graph
v = -ωA sin ωt and -ve
∴
starts at zero and goes below
top -sin, bottom cos
acceleration-time graph
a = -ω²𝑥 = -ω²A cos ωt
∴
starts at max and down below
top -cos, bottom -sin
velocity and displacement eqaution
v = ±ω√(A²-𝑥²)
± indicates direction of movement (can eb left/right/up/down)
displacement equations
- variation with time
- max
- min
- 𝑥 = A cos ωt
- equal to amplitude
- 0
velocity equations
- variation with time
- max
- min
- variation with displacement
- v = -ωA sin ωt
- ±ωA
- (extreme displacement) =0
- a = -ω²𝑥
acceleration equations
- variation with time
- max
- min
- variation with displacement
- a = -ω²A cos ωt
- (extreme displacement) = ω²A
- 0
- a = -ω²𝑥
total energy with time
constant
kinetic energy at an instant during SHM
KE = ½mv²
* find v by gradient of displacement-time graph
OR
* substitute v = ω²A sin ωt
time period for simple pendulum equation
T = 2π√l÷g
