Things to memorise for CT1

Question 1

Radian

Answer 1

Angle subtended at centre of circle by an arc of equal length to the radius

Question 2

Resonance

Answer 2

Max amplitude of vibration of object when the forced frequency is equal to the natural frequency

Question 3

Simple Harmonic Motion

Answer 3

When acceleration is directly proportional to the displacement and acceleration and displacement are in opposite directions

Question 4

Formulas for circular motion (8)

Answer 4

v = d/t = 2πr/T
a = v² / r
F𝒸= m . v²/r
(*θ in rad)
ω = 2π/T = 2πf
v = ωr
F𝒸 = mω²r
Fc = Ft + (-Fg)
∆θ = ω∆t = 2π∆t/T

Question 5

Formulas for SHM (8)

Answer 5

Fr = Fs (restoring force and spring force)
m.a = -k . x
a = -ω²x
Xₜ = Xₒsinωt (given start time [ t = 0 ] else is cos)
Vₜ = Vₒcosωt (given start time [ t = 0 ] else is sin)
aₜ = aₒsinωt (given start time [ t = 0] else is cos)
Vₜ = ± ω √Xₒ² - Xₜ²
v = ωxₒ

Question 6

Formulas for SHM MSO (4)

Answer 6

ω² = k/m
a = -k/m . x
T = 2π √m/k
ma = -2kx

Question 7

Formulas for SHM pendulum (4)

Answer 7

ω² = g/l
a = -x . g/l
T 2π √l/g
sinθ = x/l

Question 8

Energy in SHM formulas (3)

Answer 8

Eₜₒₜₐₗ = Eₖ + Eₚ
∆W = ∆Eₖ = ∆Eₚ
Eₜₒₜₐₗ = Eₖ₍ₜ₎+ Eₚ₍ₜ₎

Question 9

Damping

Answer 9

Reduction in amplitude due to resistive forces