Energy transformation always takes place between elastic potential energy and kinetic energy
The maximum of the kinetic energy occurs when the object is passing through the central position.
The maximum in potential energy occurs in the extreme position
In an undamped vibration : Emech = Ek + Ep = constant.
E mech = Ek + Ep = Ek,max = Ep,max
Emech = ½ m vmax2 = ½ m (2 π A/T)2 = ½ m (4 π2 A2 / T2) = (2 π2 A2) /T2 = 2 m π2 A2 f2
Emech = ½ C A2 (Ep in extreme position)
T = 2 π √m/C so C = 4 π2 m/T2
This gives :
Emech = ½ (4 π2 m/T2) A2 = (2 m π2 A2) T2 = 2 m π2 A2 f2
- Emech in J
- m mass in kg
- A amplitude in m
- f frequency in Hz