Question

Two different simple harmonic oscillators have the same natural frequency (f=2.00 Hz) when they are on the surface of the Earth. The first oscillator is a pendulum, the second is a vertical spring and mass. If both systems are moved to the surface of the moon (g=1.67 m/s²),

what is the new frequency of the vertical spring and mass?

Answer 1

We know that the netural frequency of the pendulum

So

...1

here g10 m/s2 ( on the earth) , f=2 Hz

put these values in equation 1

L=0.063326m

So the frequency of the pendulum on the moon

f=0.817

f=0.82 Hz

We know that the natural frequency of the spring - mass system

here K ( spring constant ) and m are constant . So

the natural frequency of the spring - mass system on the moon

f=2.0Hz