First slide

Simple harmonic motion

Question

What happens to the energy of a simple harmonic oscillator if its amplitude is doubled?

Moderate

A

$E_{2} = 2 E_{1}$
B

$E_{2} = 4 E_{1}$
C

$E_{2} = 8 E_{1}$
D

$E_{2} = E_{1}$

Solution

, $E n e r g y = E = \frac{1}{2} m ω^{2} A^{2} \Rightarrow E n e r g y α a m p l i t u d e^{2} A = a m p l i t u d e \Rightarrow \frac{E_{1}}{E_{2}} = {[\frac{A_{1}}{A_{2}}]}^{2} h e r e i n q u e s t i o n A_{2} = 2 A_{1} \Rightarrow E_{2} = 4 E_{1}$

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