OPTED OAT physics question # 21

[cis4cookie]

The question states "The amplitude of a body undergoing simple harmonic motion is doubled. Which of the following is also doubled?
a) maximum speed
b) frequency
c) total energy
d) period

They claim the answer is a) maximum speed but i was always taught and read that changing the amplitude does not change the speed but the energy of the wave. In fact if amplitude is doubled the energy should be quadrupled. Am I missing something from the question? If so, can someone explain???? i would much appreciate it, thanks

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[EyEnStein 07]

i think you misread something......heres why i think so..

correct me if im wrong im doing this from memory.

something oscillating at equilibrium position of Xo
is .. x(t) = Xo + Acos(wt + f)
which means if you want to find the speed...its derivative

v(t) = wA * sin(wt + f)...and if we want Vmax then its
just going to be Vmax = wA

according to that relationship right there when A is doubled
Vmax will also be doubled....

actually i cant think of a formula that might give energy and max speed together can you post what you were talking about with energy?

Thanks.

 

[Rusty Ryan]

I don't know if this is right but this is how I approached it.

SHM Potential Energy = 1/2kx^2
Kinetic Energy = 1/2mv^2

So 1/2kx^2 = 1/2mv^2

Neither k or m change. So essentially you have x^2=v^2

If you double amplitude you will double velocity. Plugging in numbers will confirm this I think.

 

[SonofanOpt]

1/2kA^2 is the equation for Energy.
If A is doubled, energy is quadrupled (look closely at the question).
If A is doubled, then the max velocity is also doubled. In the middle of the swing there is 0 potential energy and kinetic energy is maxed out (compared to at the top of the arc when PE is maxed and KE is at 0). The equation for KE is 1/2mv^2. Therefore by doubling A can also think of it as doubling the max velocity because of my reasoning above.

I hope I was clear enough in my explanation.