Question

If the amplitude of a simple harmonic oscillator is doubled, by what factor does the total energy increase?

a)no change

b)by a factor of two

c)by a factor of four

d)by a factor of eight

Answer 1

c)by a factor of four

Step-by-step explanation:

The total energy of a simple harmonic oscillator is given by

`E=(1)/(2)kA^2`

where

k is the spring constant of the oscillator

A is the amplitude of the motion

In this problem, the amplitude of the oscillator is doubled, so

A' = 2A

Therefore, the new total energy is

`E'=(1)/(2)k(2A)^2=4((1)/(2)kA^2)=4E`

So, the total energy increases by a factor 4.