Answer:
When both initial speed and initial displacement is doubled then amplitude will be doubled.
Explanation:
Given that :- Amplitude of simple harmonic Oscillator is doubled.
So,
Formula of Simple harmonic oscillator is ...........(1)
Where X = Position in (m,cm,km.....)
A = Amplitude in (m,cm,km.....)
F = Frequency in (Hz)
T = Time in (sec.)
Ф = Phase in (rad)
For initial displacement taking t=0 we get,
Initial displacement = .................(2)
Now taking equation (1) and differentiating it w.r.t to (t) we get
taking t=0 for initial speed then we get,
Initial speed = ...............(3)
observing equation (2) & (3) that the initial displacement and initial speed depends on the Amplitude of the Oscillator.
Hence,
when both initial speed and displacement is doubled then amplitude will be doubled.